The document outlines a thesis focused on synthesizing action sequences in planning, particularly incorporating trajectory constraints via linear temporal logic over finite traces (ltlf). It discusses the design and implementation of automata for ltlf goals and describes two approaches to planning: a traditional method and a novel simulation-based planner. The results include working implementations of various automata and planning approaches, with future work suggesting further advancements in the automata methodology.

1. Planning for Linear Time Terminating
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Candidate: Riccardo Di Stefano, 1528140
Advisor: Giuseppe De Giacomo

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https://github.com/gitRiky
https://www.linkedin.com/in/riccardo-di-stefano-439a11134/
Contacts and Links
distefanor3@gmail.com

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Introduction
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• Planning is the problem of synthesizing a sequence of
actions that leads the agent from its current state to a desired
state
• It is of interest to add trajectory constraints (typically
expressed in a fragment of LTL) while reaching the final
state. The standard PDDL3 supports these constraints, but
no planner implements them
• Recently Linear Temporal Logic over Finite Traces (LTLf)
has emerged as a formalism for expressing such constraints
• This thesis is about supporting trajectory constraints in real
planners

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Thesis Goals
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• Design and implement the automata construction starting from an
LTLf formula [DeGiacomoVardiIJCAI13,14,15]
– NFA
– DFA
• Formulate how to do planning for LTLf goals exploiting such
automata constructions
– Focus the attention on deterministic domains (classical planning)
– But also explore more advanced forms (FONDsp, FONDsc,PONDsp )
• Design and implement the state-of-the-art approach for planning for
LTLf goals [TorresBaierIJCAI15]
• Design and implement the automata based approach, using a new
planner [FrancesGeffnerIJCAI17] that exploits calls to code
(instead of actions) to progress
– In collaboration with Guillem Frances (UPF, Barcelona)

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Automata Construction Starting
from LTLf Formula
• Starting from an LTLf formula φ, we can build the related
automata:
• Put the formula in negative normal form (linear)
• Build the AFW (linear)
• Translate the AFW in NFA (exponential)
• Determinize the NFA (exponential)
• Given the NFA built from the LTLf formula φ, for every finite
trace π, π╞ φ iff π ∈ L (NFAφ)
• Satisfiability of an LTLf formula can be checked in PSPACE
by non-emptyness of the related NFA
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• NFA
Automata Construction Starting
from LTLf Formula
• DFA
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On-the-fly Automata
• On-the-fly automata do not build the whole automata in terms of
states and transition function
• Can be seen as a function that, given the current state s and a
propositional interpretation Π, returns the new automaton state sI
• Simply applies the delta
• Does not keep track of anything but current state
• DFA Example
Π = (a)
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Planning for LTLf Goals in Deterministic Domains
• Goal no more seen as propositional formula over fluents, but
expressed in LTLf formulas
• How to deal with LTLf goals? Using automata!
– We need to perform a step on the domain and then another step over
the goal automaton
– Transform the planning domain into automaton and compute the
intersection between this one and the automaton related to the LTLf
goal
– If we reach a final state in the obtained automaton, we have found a
plan
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• How to obtain the automata AD from the planning domain P?
• With this simple transformation
Planning for LTLf Goals in Deterministic Domains
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10. • Simple domain D
• Goal is defined as
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Example
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Torres-Baier Approach
• Compile away LTLf goal into classical goals
• Encode the automata in PDDL (not NFA, but AFW!)
• Add synchronization actions used for updating the state of
the automaton
– Two different modes: wold and sync
– The classical actions are executed in world mode;
– Synchronization actions are executed in sync mode.
• Plan of kind
where each represents a sequence of synchronization
actions
v
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Torres-Baier Approach
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Our Approach
• Possible with the usage of a simulation based planner: FS Planner
[FrancesGeffnerIJCAI17]
• It works in simulation mode using search algorithms based on
novelty
• Uses the definition of Factored State Model: a generalization w.r.t.
the declarative formalization of planning problems
– Defines action precondition, effects and cost as Black-Box procedures
– We are making no assumption about the description form.
• Simulator: factored state model
where are defined as black-box procedures
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Our Approach
• We use a procedure Pr (X, a), where X represents the state in
terms of domain state s and automaton state q and a represents the
action
– It applies the action a and changes the domain state s in sI
– Given the new state sI and the current automaton state q, computes the new
automaton state qI
• Can be seen as two sequential procedures
• We manage the second procedure externally, defining a completelly
procedural action update-automaton
– Execute the action over the domain
– Then execute update-automaton action
• When the external procedure returns a final state, we extract the
plan and we have done
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Discussion
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• Our approach works!
• Validated over sokoban domain
• Perfomance not comparable with Torres-Baier
• Highly extendable : procedural calls to code (instead of
actions) to progress
• Possibility of defining problems procedurally

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Conclusions
• Thesis results
– Implementation of the NFA/DFA (and on the fly variants) construction
from an LTLf formula
– Formulation planning for LTLf goals, by exploiting such automata
constructions
– A working implementation of [TorresBaierIJCAI15] approach
– A working implementation of our new approach on the novel planner by
Guillem Frances (UPF, Barcelona) [FrancesGeffnerIJCAI17]
• Future work
– The automata approach can be really extended to more advanced
planning forms (differently from [TorresBaierIJCAI15])
– FONDsp, FONDsc PONDsp
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