Program verification involves formally proving that a program satisfies certain properties, such as having no defects, by establishing that the program meets its specification. This is done by defining preconditions and postconditions and using weakest preconditions to reason about how the program transforms states. Testing involves running a program with sample inputs and checking that the outputs are as expected to find defects empirically.
Successive Differentiation is the process of differentiating a given function successively times and the results of such differentiation are called successive derivatives. The higher order differential coefficients are of utmost importance in scientific and engineering applications.
Lesson 8: Derivatives of Polynomials and Exponential functionsMatthew Leingang
Some of the most famous rules of the calculus of derivatives: the power rule, the sum rule, the constant multiple rule, and the number e defined so that e^x is its own derivative!
Derivatives of Trigonometric Functions, Part 2Pablo Antuna
In this presentation we find the derivative of cos(x) and then we solve two examples.
For more videos and lessons: http://www.intuitive-calculus.com/der...
Successive Differentiation is the process of differentiating a given function successively times and the results of such differentiation are called successive derivatives. The higher order differential coefficients are of utmost importance in scientific and engineering applications.
Lesson 8: Derivatives of Polynomials and Exponential functionsMatthew Leingang
Some of the most famous rules of the calculus of derivatives: the power rule, the sum rule, the constant multiple rule, and the number e defined so that e^x is its own derivative!
Derivatives of Trigonometric Functions, Part 2Pablo Antuna
In this presentation we find the derivative of cos(x) and then we solve two examples.
For more videos and lessons: http://www.intuitive-calculus.com/der...
Theorem-proving Verification of Multi-clock Synchronous Circuits on Multimoda...Shunji Nishimura
Formal verification methods for synchronous circuits are widely used, but almost all of the methods are limited to single-clock synchronous circuits. In this paper, we propose a formal verification method for multi-clock synchronous circuits. The proposed verification method is in theorem-proving manner and based on multimodal logic. We also show an example of verification of a clock switching circuit by using the method.
A Survey of functional verification techniquesIJSRD
In this paper, we present a survey of various techniques used in functional verification of industry hardware designs. Although the use of formal verification techniques has been increasing over time, there is still a need for an immediate practical solution resulting in an increased interest in hybrid verification techniques. Hybrid techniques combine formal and informal (traditional simulation based) techniques to take the advantage of both the worlds. A typical hybrid technique aims to address the verification bottleneck by enhancing the state space coverage.
Functional verification is one of the key bottlenecks in the rapid design of integrated circuits. It is estimated that verification in its entirety accounts for up to 60% of design resources, including duration, computer resources and total personnel. The three primary tools used in logic and functional verification of commercial integrated circuits are simulation (at various levels), emulation at the chip level, and formal verification.
I am Bon Leofen Currently associated with economicshomeworkhelper.com as an economics homework helper. After completing my master's at Ambrose University, I was in search of an opportunity that would expand my area of knowledge hence I decided to help students with their assignments. I have written several economics assignments to date to help students overcome numerous difficulties they face.
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GT Spotter is a user interface that unifies the search workflow in an IDE. This set of slides was used for a submission at the ESUG 2015 Innovation Awards.
I watched 1800+ TED talks. I watched all those published on ted.com. Why? Because I am a TED addict. And because each of these talks reminds me that storytelling is essential in everything we do.
Facts are important, but facts alone have no value. They have to be consumed to worthwhile. Stories make this happen by getting us involved. This applies to researching novel ways, it applies to creating products, it applies to leading people, it applies to educating kids, and it applies to marriage proposals. Essentially, it applies to anything worth doing.
Storytelling is what makes stories happen. But, storytelling is a skill, and like any skill, it can be learnt.
For example, an easy way to learn is to listen to good examples. Like TED talks. But, there are many ways to learn. And, there are even more ways to apply.
It only takes us to invest in it. Why?
Because storytelling is essential.
Moose: how to solve real problems without reading codeTudor Girba
I use this set of slides for a talk I gave at ESUG 2014.
Abstract:
Moose is a platform for software and data analysis (http://moosetechnology.org). It runs on Pharo and it can help you figure out problems around software systems.
In this talk, I show several real-life examples of how custom tools built on top of Moose helped solve concrete problems. The examples vary both in scope and in the kind of problems. For example, we talk about how we fixed a caching problem in a Java system by analyzing logs, or how we fixed a Morphic problem by means of visualization and interaction. Even if these problems are so different, all of them were solvable with one uniform set of programmable tools.
That is the power of Moose, and it is now at the fingertips of any Pharo programmer.
We cannot continue to let systems loose in the wild without any concern for how we will deal with them at a later time. Two decades ago, Richard Gabriel coined the idea of software habitability. Indeed, given that engineers spend a significant part of their active life inside software systems, it is desirable for that system to be suitable for humans to live there.
We go further and introduce the concept of software environmentalism based on a simple principle: Engineers have the right to build upon assessable systems and have the responsibility of producing assessable systems.
The emergent nature of software systemsTudor Girba
This slideshow offers an argument for how the structure of a software system has an inherently emergent nature.
More information can be found at: http://humane-assessment.com
22. P: (x = y - 2)
S: x := x + 2
Q: (x = y)
le
Examp
23. {P} S1 {Q} , {Q} S2 {R}
Sequence
{P} S1;S2 {R}
{P∧B} S1 {Q} , {P∧¬B} S2 {Q}
Conditional
{P} if B then S1 else S2 {Q}
24. P I ∧ ({I∧B} S {I}) , (I ∧ ¬B Q)
While loop
{P} while B do S end {Q}
25. P I ∧ ({I∧B} S {I}) , (I ∧ ¬B Q)
While loop
{P} while B do S end {Q}
Loop invariant I
I = property which stays true before and after every loop
0. initial condition: P I;
1. iterative (inductive) condition: {I ∧ B} s {I};
2. final condition: I ∧ ¬B Q
26. P: (x ≥ 0) ∧ (y > 0)
S: quo := 0;
rem := x;
while (y ≤ rem) do
rem = rem − y;
quo = quo + 1
end
Q: (quo ∗ y + rem = x) ∧
(0 ≤ rem < y) :
E xample inder
n d rema s
Qu otient a 2 integer
ng
o f dividi
27. while (lo < hi) {
m = (lo + hi) / 2;
if (n > m)
lo = m + 1;
else
hi = m;
}
n = lo;
ch
: bina ry sear
E xample
28. I: lo <= n ∧ n <= hi
while (lo < hi) { lo <= n ∧ n <= hi*/
/*I:
m = (lo + hi) / 2;
if (n > m) /*
in both cases: lo <= n ∧ n <= hi */
lo = m + 1; /* n > m => n >= m+1 => n >= lo */
else
hi = m; /* !(n < m) => n <= m => n <= hi */
} /* I stays true */
n = lo; /*
lo<=n ∧ n<=hi ∧
!(lo<hi) => lo==n ∧ n==hi */
ch
: bina ry sear
E xample
43. While loop
L = while (B) do S end
wp(L,Q) I ∧
=
∀y, ((B ∧ I) wp(S, I ∧ x < y))
∀y, ((¬B ∧ I) Q)
44. While loop
L = while (B) do S end
wp(L,Q) I ∧
=
∀y, ((B ∧ I) wp(S, I ∧ x < y))
∀y, ((¬B ∧ I) Q)
Loop verification
I = property which stays true before and after every loop
0. P I;
1. I∧B wp(s, I);
2. I∧¬B Q.
45. P: (x≥0) ∧ (y>0)
S: quo := 0;
rem := x;
while (y ≤ rem) do
rem = rem − y;
quo = quo + 1
end
Q: (quo∗y+rem=x) ∧ (0≤rem<y)
:
E xample inder
n d rema s
Qu otient a 2 integer
ng
o f dividi
46. P: (x≥0) ∧ (y>0)
S: quo := 0;
rem := x;
I: (quo∗y+rem=x) ∧ (rem≥0) ∧ (y>0) ∧ (x≥0)
while (y ≤ rem) do
rem = rem − y;
quo = quo + 1
end
Q: (quo∗y+rem=x) ∧ (0≤rem<y)
:
E xample inder
n d rema s
Qu otient a 2 integer
ng
o f dividi
47. P: (x≥0) ∧ (y>0)
I: (quo∗y+rem=x) ∧ (rem≥0) ∧ (y>0) ∧ (x≥0)
Q: (quo∗y+rem=x) ∧ (0≤rem<y)
(x ≥ 0) ∧ (y > 0)
(x = x) ∧ (x ≥ 0) ∧ (x ≥ 0) ∧ (y > 0)
(x=rem+y∗quo) ∧ (x≥0) ∧ (rem≥0) ∧ (y>0) ∧ (y≤rem)
(x = (rem − y) + y ∗ (quo + 1)) ∧
x ≥ 0 ∧ rem − y ≥ 0 ∧ y > 0
(x=rem+y∗quo) ∧ (x≥0) ∧ (rem≥0) ∧ (y>0) ∧ (y>rem)
(x = rem + y ∗ quo) ∧ (0 ≤ rem < y)
:
E xample tions
n condi
ve rificatio