In this work we extend the Emerson and Kahlon’s cutoff theorems for process skeletons with conjunctive guards to Parameterized Networks of Timed Automata, i.e. systems obtained by an unbounded number of Timed Automata instantiated from a finite set U_1 , ..., U_n of Timed Automata templates. In this way we aim at giving a first tool to universally verify software systems where an unknown number of software components (i.e. processes) interact with temporal constraints. It is often the case, indeed, that distributed algorithms show an heterogeneous nature, combining dynamic aspects with real-time aspects. In the paper we will also show how to model check a protocol that uses special variables storing identifiers of the participating processes (i.e. PIDs) in Timed Automata with conjunctive guards. This is non-trivial, since solutions to the parameterized verification problem often relies on the processes to be symmetric, i.e. indistinguishable. On the other side, many popular distributed algorithms make use of PIDs and thus cannot directly apply those solutions.
The document describes the event calculus framework for reasoning about events and their effects. It discusses key concepts like events, fluents, states and time in the event calculus. It also covers different types of reasoning supported in the event calculus like deductive, abductive and reactive reasoning. The document further discusses axiomatization of the event calculus in logic programming languages like Prolog and implementations like the cached event calculus. It also provides examples of applications that use the event calculus framework.
Parametrized Model Checking of Fault Tolerant Distributed Algorithms by Abstr...Iosif Itkin
The document discusses threshold automata (TA) and how they can be used to model fault-tolerant distributed algorithms (FTDAs). TA extend finite state machines with thresholds on shared variables. The document proposes constructing a TA from a control flow automaton that models the loop body of an FTDA. This is done by applying interval abstraction to local variables and enumerating symbolic paths to generate the TA rules. The TA can then be simulated using a counter system that models the processes. The counter system allows accelerated transitions where multiple processes move simultaneously.
Frechet Derivatives of Matrix Functions and ApplicationsSam Relton
This document summarizes Samuel Relton's presentation on Fréchet derivatives of matrix functions and their applications. Some key points:
1) It discusses how to define and compute Fréchet derivatives of matrix functions, which describe how small perturbations to a matrix affect the output of the function.
2) Applications include estimating sensitivity in nuclear activation models, predicting algebraic error in finite element methods, and analyzing condition numbers.
3) It presents algorithms for efficiently computing the most sensitive elements of a matrix to changes in the output of a function, with applications to finite elements.
This is a rapid fire talk that outline some of the issues around multithreaded code, some of the tools you can use to test it and how best to spend your resources doing so
Frigör möjligheterna i ditt data – fem enkla sätt att analysera data för att ...Transcendent Group
Presentation från GRC 2014 den 15 maj. Kontakta gärna talaren om du har några frågor. Hela schemat för eventet hittar du här: http://www.transcendentgroup.com/sv/har-har-du-hela-schemat-for-grc-2014/
This certificate certifies that an unnamed individual has successfully completed the requirements for PM3 Project Management Certification Level 1 as of July 7, 2015. The certificate was signed by Michele A. Caputo, Services BU PMO Director, and Suresh Vaswani, President of Dell Services, to confirm the individual's achievement.
Analysis of intelligent system design by neuro adaptive control no restrictioniaemedu
This document discusses using neuro-adaptive control to analyze the design of intelligent systems. It begins by introducing the topic and noting that conventional adaptive control techniques assume explicit system models or dynamic structures based on linear models, which may not be valid for complex nonlinear systems. Neural networks and other intelligent control approaches that do not require explicit mathematical modeling are presented as alternatives. The paper then focuses on using time-delay neural networks for system identification and control of nonlinear dynamic systems. Various neural network architectures and learning algorithms for system modeling and control are described.
Analysis of intelligent system design by neuro adaptive controliaemedu
This document summarizes the analysis of intelligent system design using neuro-adaptive control methods. It discusses using neural networks for system identification through series-parallel and parallel models. It also discusses supervised control using a neural network trained by an expert operator, inverse control using a neural network trained on the inverse system model, and neuro-adaptive control using two neural networks - one for system identification and one for control. Neuro-adaptive control allows handling nonlinear system behavior without linear approximations.
The document describes the event calculus framework for reasoning about events and their effects. It discusses key concepts like events, fluents, states and time in the event calculus. It also covers different types of reasoning supported in the event calculus like deductive, abductive and reactive reasoning. The document further discusses axiomatization of the event calculus in logic programming languages like Prolog and implementations like the cached event calculus. It also provides examples of applications that use the event calculus framework.
Parametrized Model Checking of Fault Tolerant Distributed Algorithms by Abstr...Iosif Itkin
The document discusses threshold automata (TA) and how they can be used to model fault-tolerant distributed algorithms (FTDAs). TA extend finite state machines with thresholds on shared variables. The document proposes constructing a TA from a control flow automaton that models the loop body of an FTDA. This is done by applying interval abstraction to local variables and enumerating symbolic paths to generate the TA rules. The TA can then be simulated using a counter system that models the processes. The counter system allows accelerated transitions where multiple processes move simultaneously.
Frechet Derivatives of Matrix Functions and ApplicationsSam Relton
This document summarizes Samuel Relton's presentation on Fréchet derivatives of matrix functions and their applications. Some key points:
1) It discusses how to define and compute Fréchet derivatives of matrix functions, which describe how small perturbations to a matrix affect the output of the function.
2) Applications include estimating sensitivity in nuclear activation models, predicting algebraic error in finite element methods, and analyzing condition numbers.
3) It presents algorithms for efficiently computing the most sensitive elements of a matrix to changes in the output of a function, with applications to finite elements.
This is a rapid fire talk that outline some of the issues around multithreaded code, some of the tools you can use to test it and how best to spend your resources doing so
Frigör möjligheterna i ditt data – fem enkla sätt att analysera data för att ...Transcendent Group
Presentation från GRC 2014 den 15 maj. Kontakta gärna talaren om du har några frågor. Hela schemat för eventet hittar du här: http://www.transcendentgroup.com/sv/har-har-du-hela-schemat-for-grc-2014/
This certificate certifies that an unnamed individual has successfully completed the requirements for PM3 Project Management Certification Level 1 as of July 7, 2015. The certificate was signed by Michele A. Caputo, Services BU PMO Director, and Suresh Vaswani, President of Dell Services, to confirm the individual's achievement.
Analysis of intelligent system design by neuro adaptive control no restrictioniaemedu
This document discusses using neuro-adaptive control to analyze the design of intelligent systems. It begins by introducing the topic and noting that conventional adaptive control techniques assume explicit system models or dynamic structures based on linear models, which may not be valid for complex nonlinear systems. Neural networks and other intelligent control approaches that do not require explicit mathematical modeling are presented as alternatives. The paper then focuses on using time-delay neural networks for system identification and control of nonlinear dynamic systems. Various neural network architectures and learning algorithms for system modeling and control are described.
Analysis of intelligent system design by neuro adaptive controliaemedu
This document summarizes the analysis of intelligent system design using neuro-adaptive control methods. It discusses using neural networks for system identification through series-parallel and parallel models. It also discusses supervised control using a neural network trained by an expert operator, inverse control using a neural network trained on the inverse system model, and neuro-adaptive control using two neural networks - one for system identification and one for control. Neuro-adaptive control allows handling nonlinear system behavior without linear approximations.
Parameterized Model Checking of Rendezvous SystemsFrancesco Spegni
A standard technique for solving the parameterized model
checking problem is to reduce it to the classic model checking problem of finitely many finite-state systems. This work considers some of the theoretical power and limitations of this technique. We focus on concurrent systems in which processes communicate via pairwise rendezvous, as well as the special cases of disjunctive guards and token passing; specifications are expressed in indexed temporal logic without the next operator; and the underlying network topologies are generated by suitable
Monadic Second Order Logic formulas and graph operations. First, we settle the exact computational complexity of the parameterized model checking problem for some of our concurrent systems, and establish new
decidability results for others. Second, we consider the cases that model checking the parameterized system can be reduced to model checking some fixed number of processes, the number is known as a cutoff. We
provide many cases for when such cutoffs can be computed, establish lower bounds on the size of such cutoffs, and identify cases where no cutoff exists. Third, we consider cases for which the parameterized system
is equivalent to a single finite-state system (more precisely a Buchi word automaton), and establish tight bounds on the sizes of such automata.
SEMANTIC STUDIES OF A SYNCHRONOUS APPROACH TO ACTIVITY RECOGNITIONcscpconf
Many important and critical applications such as surveillance or healthcare require some formof (human) activity recognition. Activities are usually represented by a series of actions driven and triggered by events. Recognition systems have to be real time, reactive, correct, complete, and dependable. These stringent requirements justify the use of formal methods to describe, analyze, verify, and generate effective recognition systems. Due to the large number of possible application domains, the researchers aim at building a generic recognition system. They choose the synchronous approach because it has a well-founded semantics and it ensures determinism and safe parallel composition. They propose a new language to represent activities as synchronous automata and they supply it with two complementary formal semantics. First a behavioral semantics gives a reference definition of program behavior using rewriting rules. Second, an equational semantics describes the behavior in a constructive way and can be directly implemented. This paper focuses on the description of these two semantics and their relation.
This document provides an overview of a lecture on time domain analysis of first order systems. The key topics covered include:
- Modeling systems using state-space representation and defining state, state vector, and state-space.
- Analyzing systems in the time domain by applying standard test inputs like impulse, step, ramp, and parabolic signals to determine the system response over time.
- The time response of first order systems consists of transient and steady-state responses. It is determined by applying standard inputs and using the system transfer function and properties like the time constant T and gain K.
Simultaneous State and Actuator Fault Estimation With Fuzzy Descriptor PMID a...Waqas Tariq
In this paper, Takagi-Sugeno (T-S) fuzzy descriptor proportional multiple-integral derivative (PMID) and Proportional-Derivative (PD) observer methods that can estimate the system states and actuator faults simultaneously are proposed. T-S fuzzy model is obtained by linearsing satellite/spacecraft attitude dynamics at suitable operating points. For fault estimation, actuator fault is introduced as state vector to develop augmented descriptor system and robust fuzzy PMID and PD observers are developed. Stability analysis is performed using Lyapunov direct method. The convergence conditions of state estimation error are formulated in the form of LMI (linear matrix inequality). Derivative gain, obtained using singular value decomposition of descriptor state matrix (E), gives more design degrees of freedom together with proportional and integral gains obtained from LMI. Simulation study is performed for our proposed methods.
A Software Tool for Live-Lock Avoidance in Systems Modelled Using a Class of ...IJCSEA Journal
If a manufacturing system enters into a state where a task enters into a state of suspended animation for perpetuity, we say it is in a livelocked state. In contrast, all tasks of the system remain suspended for perpetuity in a deadlocked state of the system. A livelock-free manufacturing system can never experience deadlocks, but the converse is not necessarily true. A livelock-prone manufacturing system can be regulated using a supervisory policy such that the resulting supervised system is livelock-free. If a liveness enforcing supervisory policy (LESP) prevents the occurrence of an event at given state of the manufacturing system, and every other LESP, irrespective of the implementation paradigm, prescribes the same control for that state, we say the original LESP is minimally restrictive.
This paper is about two enhancements to an existing software tool that synthesizes the minimally restrictive LESP for a manufacturing system modelled using a class of weighted Petri nets (PNs). The first enhancement is about broadening the scope of the software tool to a larger class of PNs. The second enhancement is about improving the running time of the software tool using a property identified in this paper.
We identify a class, ℋ, of general Petri net (PN) structures where the existence of a liveness enforcing supervisory policy (LESP) for an instance of this class, initialized at a marking, is sufficient to infer the existence of an LESP when the same instance is initialized at a larger marking. As a consequence, the existence of an LESP for the PN that results when a member of this class is initialized with a marking, is decidable. Additionally, the maximally permissive LESP, when it exists, can be synthesized using a software tool described in an earlier paper. We also highlight a property that plays a critical role in the speed of convergence of the iterative procedure for the synthesis of the minimally restrictive LESP, when it exits, for any instance of ℋ that uses the aforementioned software package.
MATHEMATICAL MODELING OF COMPLEX REDUNDANT SYSTEM UNDER HEAD-OF-LINE REPAIREditor IJMTER
Suppose a composite system consisting of two subsystems designated as ‘P’ and
‘Q’ connected in series. Subsystem ‘P’ consists of N non-identical units in series, while the
subsystem ‘Q’ consists of three identical components in parallel redundancy.
Sonendra kumar gupta operational readiness of a complex system under differen...Alexander Decker
This document presents a mathematical model to analyze the operational readiness of a complex system operating under different weather conditions. The system can be in one of three states - good, degraded, or failed. It can transition between states due to failures or during repairs. The failure rates are exponential and repair rates follow general time distributions. Laplace transforms are used to derive equations describing the behavior of the system over time. The long-term, steady-state probabilities of the system being in each state are also determined.
Global stabilization of a class of nonlinear system based on reduced order st...ijcisjournal
The problem of global stabilization for a class of nonlinear system is considered in this paper.The sufficient
condition of the global stabilization of this class of system is obtained by deducing thestabilization of itself
from the stabilization of its subsystems. This paper will come up with a designmethod of state feedback
control law to make this class of nonlinear system stable, and indicate the efficiency of the conclusion of
this paper via a series of examples and simulations at the end. Theresults presented in this paper improve
and generalize the corresponding results of recent works.
1. The document describes the syllabus for the course EE1354 - Modern Control Systems. It includes 5 units that cover topics like state space analysis of continuous and discrete time systems, z-transforms, nonlinear systems, and MIMO systems.
2. Key concepts discussed include state variable representation, eigenvectors and eigenvalues, solution of state equations, controllability and observability, and deriving state space models from transfer functions.
3. Methods like pole placement, state feedback, and observer design for state estimation are also covered in the context of analysis and design of control systems.
In the present work, Lyapunov stability theory, nonlinear adaptive control law and the parameter update
law were utilized to derive the state of two new chaotic reversal systems after being synchronized by the
function projective method. Using this technique allows for a scaling function instead of a constant thereby
giving a better method in applications in secure communication. Numerical simulations are presented to
demonstrate the effective nature of the proposed scheme of synchronization for the new chaotic reversal
system.
SEQUENTIAL CLUSTERING-BASED EVENT DETECTION FOR NONINTRUSIVE LOAD MONITORINGcscpconf
The problem of change-point detection has been well studied and adopted in many signal processing applications. In such applications, the informative segments of the signal are the stationary ones before and after the change-point. However, for some novel signal processing and machine learning applications such as Non-Intrusive Load Monitoring (NILM), the information contained in the non-stationary transient intervals is of equal or even more importance to the recognition process. In this paper, we introduce a novel clustering-based sequential detection of abrupt changes in an aggregate electricity consumption profile with the accurate decomposition of the input signal into stationary and non-stationary segments. We also introduce various event models in the context of clustering analysis. The proposed algorithm is applied to building-level energy profiles with promising results for the residential BLUED power dataset.
SEQUENTIAL CLUSTERING-BASED EVENT DETECTION FOR NONINTRUSIVE LOAD MONITORINGcsandit
The problem of change-point detection has been well studied and adopted in many signal processing applications. In such applications, the informative segments of the signal are the
stationary ones before and after the change-point. However, for some novel signal processing and machine learning applications such as Non-Intrusive Load Monitoring (NILM), the information contained in the non-stationary transient intervals is of equal or even more importance to the recognition process. In this paper, we introduce a novel clustering-based sequential detection of abrupt changes in an aggregate electricity consumption profile with
accurate decomposition of the input signal into stationary and non-stationary segments. We also introduce various event models in the context of clustering analysis. The proposed algorithm is applied to building-level energy profiles with promising results for the residential BLUED power dataset.
Control theorists have extensively studied stability
as well as relative stability of LTI systems. In this research
paper we attempt to answer the question. How unstable is an
unstable system? In that effort we define instability exponents
dealing with the impulse response. Using these instability
exponents, we characterize unstable systems.
An improved ant colony algorithm based onIJCI JOURNAL
This paper presents an improved chaotic ant colony system algorithm (ICACS) for solving combinatorial
optimization problems. The existing algorithms still have some imperfections, we use a combination of two
different operators to improve the performance of algorithm in this work. First, 3-opt local search is used
as a framework for the implementation of the ACS to improve the solution quality; Furthermore, chaos is
proposed in the work to modify the method of pheromone update to avoid the algorithm from dropping into
local optimum, thereby finding the favorable solutions. From the experimental results, we can conclude
that ICACS has much higher quality solutions than the original ACS, and can jump over the region of the
local optimum, and escape from the trap of a local optimum successfully and achieve the best solutions.
Therefore, it’s better and more effective algorithm for TSP.
GLOBAL CHAOS SYNCHRONIZATION OF UNCERTAIN LORENZ-STENFLO AND QI 4-D CHAOTIC S...ijistjournal
In this paper, we apply adaptive control method to derive new results for the global chaos synchronization of 4-D chaotic systems, viz. identical Lorenz-Stenflo(LS) systems (Stenflo, 2001), identical Qi systems (Qi, Chen and Du, 2005) and non-identical LS and Qi systems. In this paper, we shall assume that the parameters of both master and slave systems are unknown and we devise adaptive control schemes for synchronization using the estimates of parameters for both master and slave systems. Our adaptive synchronization schemes derived in this paper are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the adaptive control method is very effective and convenient to synchronize identical and non-identical LS and Qi systems.
Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive synchronization schemes for the identical and non-identical, uncertain LS and Qi 4-D chaotic systems.
GLOBAL CHAOS SYNCHRONIZATION OF UNCERTAIN LORENZ-STENFLO AND QI 4-D CHAOTIC S...ijistjournal
In this paper, we apply adaptive control method to derive new results for the global chaos synchronization of 4-D chaotic systems, viz. identical Lorenz-Stenflo(LS) systems (Stenflo, 2001), identical Qi systems (Qi, Chen and Du, 2005) and non-identical LS and Qi systems. In this paper, we shall assume that the parameters of both master and slave systems are unknown and we devise adaptive control schemes for synchronization using the estimates of parameters for both master and slave systems. Our adaptive synchronization schemes derived in this paper are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the adaptive control method is very effective and convenient to synchronize identical and non-identical LS and Qi systems. Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive synchronization schemes for the identical and non-identical, uncertain LS and Qi 4-D chaotic systems.
Availability of a Redundant System with Two Parallel Active Componentstheijes
This paper considers a redundant system which consists of two parallel active components. The time-to-failure
and the time-to-repair of the components follow an exponential and a general distribution, respectively. The
repairs of failed components are randomly interrupted. The time-to-interrupt is taken from an exponentially
distributed random variable and the interrupt times are generally distributed. We obtain the availability for the
system
On selection of periodic kernels parameters in time series predictioncsandit
This document discusses parameter selection for periodic kernels used in time series prediction. Periodic kernels are a type of kernel function used in kernel regression to perform nonparametric time series prediction. The document examines how the parameters of two periodic kernels - the first periodic kernel (FPK) and second periodic kernel (SPK) - influence prediction error. It presents an easy methodology for finding parameter values based on grid search. This methodology was tested on benchmark and real datasets and showed satisfactory results.
ADAPTIVE CONTROL AND SYNCHRONIZATION OF SPROTT-I SYSTEM WITH UNKNOWN PARAMETERSijscai
This paper derives new results for the adaptive control and synchronization design of the Sprott-I chaotic system (1994), when the system parameters are unknown. First, we build an adaptive controller to stabilize the Sprott-I chaotic system to its unstable equilibrium at the origin. Then we build an adaptive
synchronizer to achieve global chaos synchronization of the identical Sprott-I chaotic systems with unknown parameters. The results derived for adaptive stabilization and adaptive synchronization for the Sprott-I chaotic system have been established using adaptive control theory and Lyapunov stability
theory. Numerical simulations have been shown to demonstrate the effectiveness of the adaptive control and synchronization schemes derived in this paper for the Sprott-I chaotic system.
The debris of the ‘last major merger’ is dynamically youngSérgio Sacani
The Milky Way’s (MW) inner stellar halo contains an [Fe/H]-rich component with highly eccentric orbits, often referred to as the
‘last major merger.’ Hypotheses for the origin of this component include Gaia-Sausage/Enceladus (GSE), where the progenitor
collided with the MW proto-disc 8–11 Gyr ago, and the Virgo Radial Merger (VRM), where the progenitor collided with the
MW disc within the last 3 Gyr. These two scenarios make different predictions about observable structure in local phase space,
because the morphology of debris depends on how long it has had to phase mix. The recently identified phase-space folds in Gaia
DR3 have positive caustic velocities, making them fundamentally different than the phase-mixed chevrons found in simulations
at late times. Roughly 20 per cent of the stars in the prograde local stellar halo are associated with the observed caustics. Based
on a simple phase-mixing model, the observed number of caustics are consistent with a merger that occurred 1–2 Gyr ago.
We also compare the observed phase-space distribution to FIRE-2 Latte simulations of GSE-like mergers, using a quantitative
measurement of phase mixing (2D causticality). The observed local phase-space distribution best matches the simulated data
1–2 Gyr after collision, and certainly not later than 3 Gyr. This is further evidence that the progenitor of the ‘last major merger’
did not collide with the MW proto-disc at early times, as is thought for the GSE, but instead collided with the MW disc within
the last few Gyr, consistent with the body of work surrounding the VRM.
The technology uses reclaimed CO₂ as the dyeing medium in a closed loop process. When pressurized, CO₂ becomes supercritical (SC-CO₂). In this state CO₂ has a very high solvent power, allowing the dye to dissolve easily.
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Parameterized Model Checking of Rendezvous SystemsFrancesco Spegni
A standard technique for solving the parameterized model
checking problem is to reduce it to the classic model checking problem of finitely many finite-state systems. This work considers some of the theoretical power and limitations of this technique. We focus on concurrent systems in which processes communicate via pairwise rendezvous, as well as the special cases of disjunctive guards and token passing; specifications are expressed in indexed temporal logic without the next operator; and the underlying network topologies are generated by suitable
Monadic Second Order Logic formulas and graph operations. First, we settle the exact computational complexity of the parameterized model checking problem for some of our concurrent systems, and establish new
decidability results for others. Second, we consider the cases that model checking the parameterized system can be reduced to model checking some fixed number of processes, the number is known as a cutoff. We
provide many cases for when such cutoffs can be computed, establish lower bounds on the size of such cutoffs, and identify cases where no cutoff exists. Third, we consider cases for which the parameterized system
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SEMANTIC STUDIES OF A SYNCHRONOUS APPROACH TO ACTIVITY RECOGNITIONcscpconf
Many important and critical applications such as surveillance or healthcare require some formof (human) activity recognition. Activities are usually represented by a series of actions driven and triggered by events. Recognition systems have to be real time, reactive, correct, complete, and dependable. These stringent requirements justify the use of formal methods to describe, analyze, verify, and generate effective recognition systems. Due to the large number of possible application domains, the researchers aim at building a generic recognition system. They choose the synchronous approach because it has a well-founded semantics and it ensures determinism and safe parallel composition. They propose a new language to represent activities as synchronous automata and they supply it with two complementary formal semantics. First a behavioral semantics gives a reference definition of program behavior using rewriting rules. Second, an equational semantics describes the behavior in a constructive way and can be directly implemented. This paper focuses on the description of these two semantics and their relation.
This document provides an overview of a lecture on time domain analysis of first order systems. The key topics covered include:
- Modeling systems using state-space representation and defining state, state vector, and state-space.
- Analyzing systems in the time domain by applying standard test inputs like impulse, step, ramp, and parabolic signals to determine the system response over time.
- The time response of first order systems consists of transient and steady-state responses. It is determined by applying standard inputs and using the system transfer function and properties like the time constant T and gain K.
Simultaneous State and Actuator Fault Estimation With Fuzzy Descriptor PMID a...Waqas Tariq
In this paper, Takagi-Sugeno (T-S) fuzzy descriptor proportional multiple-integral derivative (PMID) and Proportional-Derivative (PD) observer methods that can estimate the system states and actuator faults simultaneously are proposed. T-S fuzzy model is obtained by linearsing satellite/spacecraft attitude dynamics at suitable operating points. For fault estimation, actuator fault is introduced as state vector to develop augmented descriptor system and robust fuzzy PMID and PD observers are developed. Stability analysis is performed using Lyapunov direct method. The convergence conditions of state estimation error are formulated in the form of LMI (linear matrix inequality). Derivative gain, obtained using singular value decomposition of descriptor state matrix (E), gives more design degrees of freedom together with proportional and integral gains obtained from LMI. Simulation study is performed for our proposed methods.
A Software Tool for Live-Lock Avoidance in Systems Modelled Using a Class of ...IJCSEA Journal
If a manufacturing system enters into a state where a task enters into a state of suspended animation for perpetuity, we say it is in a livelocked state. In contrast, all tasks of the system remain suspended for perpetuity in a deadlocked state of the system. A livelock-free manufacturing system can never experience deadlocks, but the converse is not necessarily true. A livelock-prone manufacturing system can be regulated using a supervisory policy such that the resulting supervised system is livelock-free. If a liveness enforcing supervisory policy (LESP) prevents the occurrence of an event at given state of the manufacturing system, and every other LESP, irrespective of the implementation paradigm, prescribes the same control for that state, we say the original LESP is minimally restrictive.
This paper is about two enhancements to an existing software tool that synthesizes the minimally restrictive LESP for a manufacturing system modelled using a class of weighted Petri nets (PNs). The first enhancement is about broadening the scope of the software tool to a larger class of PNs. The second enhancement is about improving the running time of the software tool using a property identified in this paper.
We identify a class, ℋ, of general Petri net (PN) structures where the existence of a liveness enforcing supervisory policy (LESP) for an instance of this class, initialized at a marking, is sufficient to infer the existence of an LESP when the same instance is initialized at a larger marking. As a consequence, the existence of an LESP for the PN that results when a member of this class is initialized with a marking, is decidable. Additionally, the maximally permissive LESP, when it exists, can be synthesized using a software tool described in an earlier paper. We also highlight a property that plays a critical role in the speed of convergence of the iterative procedure for the synthesis of the minimally restrictive LESP, when it exits, for any instance of ℋ that uses the aforementioned software package.
MATHEMATICAL MODELING OF COMPLEX REDUNDANT SYSTEM UNDER HEAD-OF-LINE REPAIREditor IJMTER
Suppose a composite system consisting of two subsystems designated as ‘P’ and
‘Q’ connected in series. Subsystem ‘P’ consists of N non-identical units in series, while the
subsystem ‘Q’ consists of three identical components in parallel redundancy.
Sonendra kumar gupta operational readiness of a complex system under differen...Alexander Decker
This document presents a mathematical model to analyze the operational readiness of a complex system operating under different weather conditions. The system can be in one of three states - good, degraded, or failed. It can transition between states due to failures or during repairs. The failure rates are exponential and repair rates follow general time distributions. Laplace transforms are used to derive equations describing the behavior of the system over time. The long-term, steady-state probabilities of the system being in each state are also determined.
Global stabilization of a class of nonlinear system based on reduced order st...ijcisjournal
The problem of global stabilization for a class of nonlinear system is considered in this paper.The sufficient
condition of the global stabilization of this class of system is obtained by deducing thestabilization of itself
from the stabilization of its subsystems. This paper will come up with a designmethod of state feedback
control law to make this class of nonlinear system stable, and indicate the efficiency of the conclusion of
this paper via a series of examples and simulations at the end. Theresults presented in this paper improve
and generalize the corresponding results of recent works.
1. The document describes the syllabus for the course EE1354 - Modern Control Systems. It includes 5 units that cover topics like state space analysis of continuous and discrete time systems, z-transforms, nonlinear systems, and MIMO systems.
2. Key concepts discussed include state variable representation, eigenvectors and eigenvalues, solution of state equations, controllability and observability, and deriving state space models from transfer functions.
3. Methods like pole placement, state feedback, and observer design for state estimation are also covered in the context of analysis and design of control systems.
In the present work, Lyapunov stability theory, nonlinear adaptive control law and the parameter update
law were utilized to derive the state of two new chaotic reversal systems after being synchronized by the
function projective method. Using this technique allows for a scaling function instead of a constant thereby
giving a better method in applications in secure communication. Numerical simulations are presented to
demonstrate the effective nature of the proposed scheme of synchronization for the new chaotic reversal
system.
SEQUENTIAL CLUSTERING-BASED EVENT DETECTION FOR NONINTRUSIVE LOAD MONITORINGcscpconf
The problem of change-point detection has been well studied and adopted in many signal processing applications. In such applications, the informative segments of the signal are the stationary ones before and after the change-point. However, for some novel signal processing and machine learning applications such as Non-Intrusive Load Monitoring (NILM), the information contained in the non-stationary transient intervals is of equal or even more importance to the recognition process. In this paper, we introduce a novel clustering-based sequential detection of abrupt changes in an aggregate electricity consumption profile with the accurate decomposition of the input signal into stationary and non-stationary segments. We also introduce various event models in the context of clustering analysis. The proposed algorithm is applied to building-level energy profiles with promising results for the residential BLUED power dataset.
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The problem of change-point detection has been well studied and adopted in many signal processing applications. In such applications, the informative segments of the signal are the
stationary ones before and after the change-point. However, for some novel signal processing and machine learning applications such as Non-Intrusive Load Monitoring (NILM), the information contained in the non-stationary transient intervals is of equal or even more importance to the recognition process. In this paper, we introduce a novel clustering-based sequential detection of abrupt changes in an aggregate electricity consumption profile with
accurate decomposition of the input signal into stationary and non-stationary segments. We also introduce various event models in the context of clustering analysis. The proposed algorithm is applied to building-level energy profiles with promising results for the residential BLUED power dataset.
Control theorists have extensively studied stability
as well as relative stability of LTI systems. In this research
paper we attempt to answer the question. How unstable is an
unstable system? In that effort we define instability exponents
dealing with the impulse response. Using these instability
exponents, we characterize unstable systems.
An improved ant colony algorithm based onIJCI JOURNAL
This paper presents an improved chaotic ant colony system algorithm (ICACS) for solving combinatorial
optimization problems. The existing algorithms still have some imperfections, we use a combination of two
different operators to improve the performance of algorithm in this work. First, 3-opt local search is used
as a framework for the implementation of the ACS to improve the solution quality; Furthermore, chaos is
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Parameterized Model Checking for Timed Systems with Conjunctive Guards
1. Parameterized Model-Checking for Timed Systems with
Conjunctive Guards
Luca Spalazzi, and Francesco Spegni
fspalazzi,spegnig@dii.univpm.it
DII @ UnivPM, Ancona, Italy
Veri
2. ed Software: Theories, Tools and Experiments
18th July 2014
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 1 / 31
4. cation
4 Cuto Theorems
5 An example
6 Final discussion
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 2 / 31
15. cation
OUTPUT:
True: if 8(n1; : : : ; nk ) : P(n1)jj : : : jjP(nk ) j=
False: otherwise (+ counterexample)
Undecidable in general
see. (Apt and Kozen, '86), parameterized reachability
Relevance to Software Veri
16. cation
(Fault Tolerant) Distributed Algorithms
Security Protocols
. . .
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 3 / 31
17. Intro
Cuto
upper bound to the number of copies for each process template
Cuto Theorem for Untimed Systems with Conjunctive/Disjunctive
guards (Emerson and Kahlon, 2003)
plus: automatic, modular approach (reuse model checkers)
minus: complexity may be high (i.e. non optimal)
until now, no work on cuto for timed systems (that we know. . . )
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 4 / 31
22. cation
4 Cuto Theorems
5 An example
6 Final discussion
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 6 / 31
23. System Model
Parameterized Networks of Timed Automata - 1
Timed Automaton:
P = (S; ^s; C; ; ; I )
S: set of states
^s 2 S: initial state
C: set of clock variables
: set of boolean expressions on S
S TCC 2C S: transition relation
I : S ! TCC : state invariant mapping
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 7 / 31
24. System Model
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 8 / 31
25. System Model
Parameterized Networks of Timed Automata - 2
Network of TA with Conjunctive Guards:
P(n1)
jj 1 : : : jjP(nm)
m
guards in l have the form:
^
mnl
m6=i
(^sm
l _ pm
l _ _ qm
l ) ^
^
hk
h6=l
(
^
jnh
(^sj
h _ pj
h _ _ qj
h))
l ; : : : ; qm
l 2 Sm
l , pj
where pm
h; : : : ; qj
h 2 Sj
h, and ^sm
l , ^sj
h are the initial
l and Uj
states of Um
h, respectively.
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 9 / 31
26. System Model
Parameterized Networks of Timed Automata - 2
Network of TA with Conjunctive Guards:
P(n1)
jj 1 : : : jjP(nm)
m
guards in l have the form:
^
mnl
m6=i
(^sm
l _ pm
l _ _ qm
l ) ^
^
hk
h6=l
(
^
jnh
(^sj
h _ pj
h _ _ qj
h))
l ; : : : ; qm
l 2 Sm
l , pj
where pm
h; : : : ; qj
h 2 Sj
h, and ^sm
l , ^sj
h are the initial
l and Uj
states of Um
h, respectively.
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 9 / 31
28. guration:
(hs1; u1i; : : : ; hsm; umi)
sl : [1::nl ] ! Sl maps an instance to its current state, and
ul : [1::nl ] ! (Cl ! R0), maps an instance to its clock function
Continuous time model
Steps
delay: clocks update, local states unchanged
local: local state changes instantaneously, guard must hold
State invariants: 8i 2 [1; nl ] : ul (i) j= I i
l (sl (i ))
Interleaving semantics
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 10 / 31
30. guration:
(hs1; u1i; : : : ; hsm; umi)
sl : [1::nl ] ! Sl maps an instance to its current state, and
ul : [1::nl ] ! (Cl ! R0), maps an instance to its clock function
Continuous time model
Steps
delay: clocks update, local states unchanged
local: local state changes instantaneously, guard must hold
State invariants: 8i 2 [1; nl ] : ul (i) j= I i
l (sl (i ))
Interleaving semantics
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 10 / 31
32. guration:
(hs1; u1i; : : : ; hsm; umi)
sl : [1::nl ] ! Sl maps an instance to its current state, and
ul : [1::nl ] ! (Cl ! R0), maps an instance to its clock function
Continuous time model
Steps
delay: clocks update, local states unchanged
local: local state changes instantaneously, guard must hold
State invariants: 8i 2 [1; nl ] : ul (i) j= I i
l (sl (i ))
Interleaving semantics
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 10 / 31
34. guration:
(hs1; u1i; : : : ; hsm; umi)
sl : [1::nl ] ! Sl maps an instance to its current state, and
ul : [1::nl ] ! (Cl ! R0), maps an instance to its clock function
Continuous time model
Steps
delay: clocks update, local states unchanged
local: local state changes instantaneously, guard must hold
State invariants: 8i 2 [1; nl ] : ul (i) j= I i
l (sl (i ))
Interleaving semantics
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 10 / 31
36. guration:
(hs1; u1i; : : : ; hsm; umi)
sl : [1::nl ] ! Sl maps an instance to its current state, and
ul : [1::nl ] ! (Cl ! R0), maps an instance to its clock function
Continuous time model
Steps
delay: clocks update, local states unchanged
local: local state changes instantaneously, guard must hold
State invariants: 8i 2 [1; nl ] : ul (i) j= I i
l (sl (i ))
Interleaving semantics
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 10 / 31
39. cation
4 Cuto Theorems
5 An example
6 Final discussion
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 11 / 31
45. cation
ITCTL? - Semantics
Semantics
c j= V
p(il ) i p(il ) = state(c(l ; i))
c j=
il
(il ) i 8i 2 [1; nl ] : c j= (il )
c j= A i 8 2 paths(c) : j=
j= 1 Uc 2 i 9t0 c : bt0 j= 2 ^
8t 2 [0; t0) : bt j= 1
where
c is a con
46. guration
is a path; bt is a sux originating at time t
2 f;; ; ;=g
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 13 / 31
48. cation
4 Cuto Theorems
5 An example
6 Final discussion
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 14 / 31
49. Cuto Theorems
Cuto Theorem for NTA with DG - 1
Monotonicity Lemma
(i) P(1)
1 jjP(n)
2 j= E(12) ) P(1)
1 jjP(n+1)
2 j= E(12)
(ii) P(1)
1 jjP(n)
2 j= E(11) ) P(1)
1 jjP(n+1)
2 j= E(11)
where is a MITL formula
Proof idea: in the big system, every instance behaves as in the
small one, except the (n + 1)-th that stutters in its initial state
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 15 / 31
50. Cuto Theorems
Cuto Theorem for NTA with DG - 1
Monotonicity Lemma
(i) P(1)
1 jjP(n)
2 j= E(12) ) P(1)
1 jjP(n+1)
2 j= E(12)
(ii) P(1)
1 jjP(n)
2 j= E(11) ) P(1)
1 jjP(n+1)
2 j= E(11)
where is a MITL formula
Proof idea: in the big system, every instance behaves as in the
small one, except the (n + 1)-th that stutters in its initial state
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 15 / 31
51. Cuto Theorems
Cuto Theorem for NTA with DG - 2
Bounding Lemma
(i ) 8n c2:P(1)
1 jjP(n)
2 j= E(12) i P(1)
1 jjP(c2)
2 j= E(12)
(ii) 8n c1:P(1)
1 jjP(n)
2 j= E(11) i P(1)
1 jjP(c1)
2 j= E(11)
where
is a MITL formula,
c1 = 2jP2j and c2 = 2jP2j + 1
Proof idea: given a path x in the big system,
52. nd a path y in the
small one, such that:
instances 11 and 12 are mimicked exactly
instance 22 is any instance with in
53. nite behavior
instances i2, for i 3 are for detecting deadlock
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 16 / 31
54. Cuto Theorems
Cuto Theorem for NTA with DG - 2
Bounding Lemma
(i ) 8n c2:P(1)
1 jjP(n)
2 j= E(12) i P(1)
1 jjP(c2)
2 j= E(12)
(ii) 8n c1:P(1)
1 jjP(n)
2 j= E(11) i P(1)
1 jjP(c1)
2 j= E(11)
where
is a MITL formula,
c1 = 2jP2j and c2 = 2jP2j + 1
Proof idea: given a path x in the big system,
55. nd a path y in the
small one, such that:
instances 11 and 12 are mimicked exactly
instance 22 is any instance with in
56. nite behavior
instances i2, for i 3 are for detecting deadlock
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 16 / 31
57. Cuto Theorems
Cuto Theorem for NTA with DG - 3
Cuto Theorem
8(n1; : : : ; nk ) : P(n1)
1 jj : : : jjP(nk )
k j= i
8(d1; : : : ; dk ) (c1; : : : ; ck ) : P(d1)
1 jj : : : jjP(dk )
k j=
Follows from Monotonicity Lemma, Bounding Lemma and duality of
E/A path quanti
58. ers
Trace equivalence of small and big systems (restricted to 1st
instance)
Smaller cutos:
c1 = 1; c2 = 2 for Einf=Ainf
c1 = 1; c2 = 1 for E
72. n
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 17 / 31
73. Cuto Theorems
Complexity of Parameterized Model Checking Problem
PMCP for Timed Systems with Conjunctive Guards is:
UNDECIDABLE for 2 ITCTL?
DECIDABLE and 2-EXPSPACE for 2 IMITL
DECIDABLE and EXPSPACE for 2 TCTL
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 18 / 31
74. An example
You are here...
1 Intro
2 System Model
3 Speci
75. cation
4 Cuto Theorems
5 An example
6 Final discussion
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 19 / 31
76. An example
Example: Fischer's Protocol - 1
v = 0; c := 0 v := PID; c := 0 v = PID; c k
start init b1 b2 cs
v6= PID; c k
v := 0
Standard process de
77. nition in Fischer's protocol
c: local clock variable
k: timeout constant
v: shared integer variable
PID: integer constant, unique for every process
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 20 / 31
78. An example
Example: Fischer's Protocol - 2
Abstracting PID variable
v1
start v0
v2
Figure: V: a shared variable
start dipid mypid
Figure: W: a process-centric view of a
shared PID variable
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 21 / 31
79. An example
Example: Fischer's Protocol - 3
Resulting model: P00 = (P W) (with conjunctive guards)
P: standard process de
80. nition in Fischer's protocol
W: process abstraction of shared PID variable
conjunctive guards: obtained translating guards (v = PID, v6= PID)
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 22 / 31
82. cation: removed states without incoming transition
Lower the required cuto (9 = 2 * 4 + 1)
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 23 / 31
84. cation results
FVormula Out Time (s) Mem (M)
Vi EF(CS mypid(i)) T 0.01 155.2
Vi6=j AG!(CS mypid(i ) ^ CS mypid(j)) T 30.1 155.2
i AF(CS mypid(i)) F 0.59 155.2
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 24 / 31
86. cation
4 Cuto Theorems
5 An example
6 Final discussion
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 25 / 31
87. Final discussion
Some take-home messages
Cuto theorems are useful for verifying real-time systems in practice
May be non optimal :-/
Systems are too complex (i.e. infeasible)
Veri
89. ned (i.e. abstractions . . . )
Conjunctive guards can be used to abstract PID variables
For the future:
Extend cuto for timed systems with disjunctive guards
(pairwise rendezvous don't admit cuto!)
Explore systems mixing templates with CG/DG
(but not arbitrary boolean formula: PMCP is UNDECIDABLE!)
Compute cuto for speci
90. c process templates
Verify more complex benchmarks/real-world examples
(suggestions are welcome :-))
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 26 / 31
91. Final discussion
Some take-home messages
Cuto theorems are useful for verifying real-time systems in practice
May be non optimal :-/
Systems are too complex (i.e. infeasible)
Veri
93. ned (i.e. abstractions . . . )
Conjunctive guards can be used to abstract PID variables
For the future:
Extend cuto for timed systems with disjunctive guards
(pairwise rendezvous don't admit cuto!)
Explore systems mixing templates with CG/DG
(but not arbitrary boolean formula: PMCP is UNDECIDABLE!)
Compute cuto for speci
94. c process templates
Verify more complex benchmarks/real-world examples
(suggestions are welcome :-))
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 26 / 31
95. Final discussion
Some take-home messages
Cuto theorems are useful for verifying real-time systems in practice
May be non optimal :-/
Systems are too complex (i.e. infeasible)
Veri
97. ned (i.e. abstractions . . . )
Conjunctive guards can be used to abstract PID variables
For the future:
Extend cuto for timed systems with disjunctive guards
(pairwise rendezvous don't admit cuto!)
Explore systems mixing templates with CG/DG
(but not arbitrary boolean formula: PMCP is UNDECIDABLE!)
Compute cuto for speci
98. c process templates
Verify more complex benchmarks/real-world examples
(suggestions are welcome :-))
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 26 / 31
99. Final discussion
Some take-home messages
Cuto theorems are useful for verifying real-time systems in practice
May be non optimal :-/
Systems are too complex (i.e. infeasible)
Veri
101. ned (i.e. abstractions . . . )
Conjunctive guards can be used to abstract PID variables
For the future:
Extend cuto for timed systems with disjunctive guards
(pairwise rendezvous don't admit cuto!)
Explore systems mixing templates with CG/DG
(but not arbitrary boolean formula: PMCP is UNDECIDABLE!)
Compute cuto for speci
102. c process templates
Verify more complex benchmarks/real-world examples
(suggestions are welcome :-))
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 26 / 31
103. Final discussion
Some take-home messages
Cuto theorems are useful for verifying real-time systems in practice
May be non optimal :-/
Systems are too complex (i.e. infeasible)
Veri
105. ned (i.e. abstractions . . . )
Conjunctive guards can be used to abstract PID variables
For the future:
Extend cuto for timed systems with disjunctive guards
(pairwise rendezvous don't admit cuto!)
Explore systems mixing templates with CG/DG
(but not arbitrary boolean formula: PMCP is UNDECIDABLE!)
Compute cuto for speci
106. c process templates
Verify more complex benchmarks/real-world examples
(suggestions are welcome :-))
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 26 / 31
107. Final discussion
Some take-home messages
Cuto theorems are useful for verifying real-time systems in practice
May be non optimal :-/
Systems are too complex (i.e. infeasible)
Veri
109. ned (i.e. abstractions . . . )
Conjunctive guards can be used to abstract PID variables
For the future:
Extend cuto for timed systems with disjunctive guards
(pairwise rendezvous don't admit cuto!)
Explore systems mixing templates with CG/DG
(but not arbitrary boolean formula: PMCP is UNDECIDABLE!)
Compute cuto for speci
110. c process templates
Verify more complex benchmarks/real-world examples
(suggestions are welcome :-))
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 26 / 31
111. Final discussion
Some take-home messages
Cuto theorems are useful for verifying real-time systems in practice
May be non optimal :-/
Systems are too complex (i.e. infeasible)
Veri
113. ned (i.e. abstractions . . . )
Conjunctive guards can be used to abstract PID variables
For the future:
Extend cuto for timed systems with disjunctive guards
(pairwise rendezvous don't admit cuto!)
Explore systems mixing templates with CG/DG
(but not arbitrary boolean formula: PMCP is UNDECIDABLE!)
Compute cuto for speci
114. c process templates
Verify more complex benchmarks/real-world examples
(suggestions are welcome :-))
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 26 / 31
115. Final discussion
Some take-home messages
Cuto theorems are useful for verifying real-time systems in practice
May be non optimal :-/
Systems are too complex (i.e. infeasible)
Veri
117. ned (i.e. abstractions . . . )
Conjunctive guards can be used to abstract PID variables
For the future:
Extend cuto for timed systems with disjunctive guards
(pairwise rendezvous don't admit cuto!)
Explore systems mixing templates with CG/DG
(but not arbitrary boolean formula: PMCP is UNDECIDABLE!)
Compute cuto for speci
118. c process templates
Verify more complex benchmarks/real-world examples
(suggestions are welcome :-))
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 26 / 31
119. Final discussion
Some take-home messages
Cuto theorems are useful for verifying real-time systems in practice
May be non optimal :-/
Systems are too complex (i.e. infeasible)
Veri
121. ned (i.e. abstractions . . . )
Conjunctive guards can be used to abstract PID variables
For the future:
Extend cuto for timed systems with disjunctive guards
(pairwise rendezvous don't admit cuto!)
Explore systems mixing templates with CG/DG
(but not arbitrary boolean formula: PMCP is UNDECIDABLE!)
Compute cuto for speci
122. c process templates
Verify more complex benchmarks/real-world examples
(suggestions are welcome :-))
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 26 / 31
123. Final discussion
Some take-home messages
Cuto theorems are useful for verifying real-time systems in practice
May be non optimal :-/
Systems are too complex (i.e. infeasible)
Veri
125. ned (i.e. abstractions . . . )
Conjunctive guards can be used to abstract PID variables
For the future:
Extend cuto for timed systems with disjunctive guards
(pairwise rendezvous don't admit cuto!)
Explore systems mixing templates with CG/DG
(but not arbitrary boolean formula: PMCP is UNDECIDABLE!)
Compute cuto for speci
126. c process templates
Verify more complex benchmarks/real-world examples
(suggestions are welcome :-))
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 26 / 31
128. sh
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 27 / 31
129. Some approaches to PMCP
Abstraction (precise, CEGAR, . . . )
Proof theoretic
Inductive invariants
Satis
130. ability Modulo Theories
plus: semi-automatic
minus: semi-automatic
Cuto
upper bound to the number of copies for each process template
plus: automatic, modular approach (reuse model checkers)
minus: complexity may be high (i.e. non optimal)
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 28 / 31
132. cation of Timed Systems
Several formalisms (Timed Automata, Hybrid Systems, . . . )
Some results on parameterized veri
133. cation
Controller state reachability is undecidable in multi-clock dense timed
networks (Abdulla et al., 2004)
Controller state reachability is decidable in multi-clock discrete timed
networks (Abdulla et al., 2004)
Recurrent state problem is undecidable in timed networks (Abdulla and
Jonsson, 2003)
All these results require synchronous rendezvous . . .
No results on cutos for timed systems
No rendezvous (parameterized rendezvous systems don't have cuto)
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 29 / 31
135. cation of Timed Systems
Several formalisms (Timed Automata, Hybrid Systems, . . . )
Some results on parameterized veri
136. cation
Controller state reachability is undecidable in multi-clock dense timed
networks (Abdulla et al., 2004)
Controller state reachability is decidable in multi-clock discrete timed
networks (Abdulla et al., 2004)
Recurrent state problem is undecidable in timed networks (Abdulla and
Jonsson, 2003)
All these results require synchronous rendezvous . . .
No results on cutos for timed systems
No rendezvous (parameterized rendezvous systems don't have cuto)
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 29 / 31
138. cation of Timed Systems
Several formalisms (Timed Automata, Hybrid Systems, . . . )
Some results on parameterized veri
139. cation
Controller state reachability is undecidable in multi-clock dense timed
networks (Abdulla et al., 2004)
Controller state reachability is decidable in multi-clock discrete timed
networks (Abdulla et al., 2004)
Recurrent state problem is undecidable in timed networks (Abdulla and
Jonsson, 2003)
All these results require synchronous rendezvous . . .
No results on cutos for timed systems
No rendezvous (parameterized rendezvous systems don't have cuto)
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 29 / 31
141. cation of Timed Systems
Several formalisms (Timed Automata, Hybrid Systems, . . . )
Some results on parameterized veri
142. cation
Controller state reachability is undecidable in multi-clock dense timed
networks (Abdulla et al., 2004)
Controller state reachability is decidable in multi-clock discrete timed
networks (Abdulla et al., 2004)
Recurrent state problem is undecidable in timed networks (Abdulla and
Jonsson, 2003)
All these results require synchronous rendezvous . . .
No results on cutos for timed systems
No rendezvous (parameterized rendezvous systems don't have cuto)
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 29 / 31
143. Cuto for Timed Systems - Simple solution
reuse (untimed) cuto theorem
1 design timed process template
2 apply clock/zone abstraction
3 compute cuto on abstract states and instantiate
4 model check
plus: no need for theoretical results
minus: high cuto, cannot reuse model checkers for timed systems
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 30 / 31
144. Cuto for Timed Systems - Simple solution
reuse (untimed) cuto theorem
1 design timed process template
2 apply clock/zone abstraction
3 compute cuto on abstract states and instantiate
4 model check
plus: no need for theoretical results
minus: high cuto, cannot reuse model checkers for timed systems
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 30 / 31
145. Cuto for Timed Systems - Simple solution
reuse (untimed) cuto theorem
1 design timed process template
2 apply clock/zone abstraction
3 compute cuto on abstract states and instantiate
4 model check
plus: no need for theoretical results
minus: high cuto, cannot reuse model checkers for timed systems
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 30 / 31
146. Cuto for Timed Systems - Alternative solution
prove timed cuto theorems
1 design timed process template
2 compute cuto on original template and instantiate
3 model check
plus: the timed cuto theorems can be reused, can reuse existing
model checkers for timed systems, the cuto is smaller
minus: required some theoretical eort
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 31 / 31
147. Cuto for Timed Systems - Alternative solution
prove timed cuto theorems
1 design timed process template
2 compute cuto on original template and instantiate
3 model check
plus: the timed cuto theorems can be reused, can reuse existing
model checkers for timed systems, the cuto is smaller
minus: required some theoretical eort
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 31 / 31
148. Cuto for Timed Systems - Alternative solution
prove timed cuto theorems
1 design timed process template
2 compute cuto on original template and instantiate
3 model check
plus: the timed cuto theorems can be reused, can reuse existing
model checkers for timed systems, the cuto is smaller
minus: required some theoretical eort
L. Spalazzi, F. Spegni (UnivPM, Ancona) PMC for Timed Systems with Conj. Guards VSTTE 2014 31 / 31