9 research outputs found
The Planning Spectrum - One, Two, Three, Infinity
Linear Temporal Logic (LTL) is widely used for defining conditions on the
execution paths of dynamic systems. In the case of dynamic systems that allow
for nondeterministic evolutions, one has to specify, along with an LTL formula
f, which are the paths that are required to satisfy the formula. Two extreme
cases are the universal interpretation A.f, which requires that the formula be
satisfied for all execution paths, and the existential interpretation E.f,
which requires that the formula be satisfied for some execution path.
When LTL is applied to the definition of goals in planning problems on
nondeterministic domains, these two extreme cases are too restrictive. It is
often impossible to develop plans that achieve the goal in all the
nondeterministic evolutions of a system, and it is too weak to require that the
goal is satisfied by some execution.
In this paper we explore alternative interpretations of an LTL formula that
are between these extreme cases. We define a new language that permits an
arbitrary combination of the A and E quantifiers, thus allowing, for instance,
to require that each finite execution can be extended to an execution
satisfying an LTL formula (AE.f), or that there is some finite execution whose
extensions all satisfy an LTL formula (EA.f). We show that only eight of these
combinations of path quantifiers are relevant, corresponding to an alternation
of the quantifiers of length one (A and E), two (AE and EA), three (AEA and
EAE), and infinity ((AE)* and (EA)*). We also present a planning algorithm for
the new language that is based on an automata-theoretic approach, and study its
complexity
Extensional and Intensional Strategies
This paper is a contribution to the theoretical foundations of strategies. We
first present a general definition of abstract strategies which is extensional
in the sense that a strategy is defined explicitly as a set of derivations of
an abstract reduction system. We then move to a more intensional definition
supporting the abstract view but more operational in the sense that it
describes a means for determining such a set. We characterize the class of
extensional strategies that can be defined intensionally. We also give some
hints towards a logical characterization of intensional strategies and propose
a few challenging perspectives
Fully Observable Non-deterministic Planning as Assumption-Based Reactive Synthesis
We contribute to recent efforts in relating two approaches to automatic synthesis, namely, automated planning and discrete reactive synthesis. First, we develop a declarative characterization of the standard “fairness” assumption on environments in non-deterministic planning, and show that strong-cyclic plans are correct solution concepts for fair environments. This complements, and arguably completes, the existing foundational work on non-deterministic planning, which focuses on characterizing (and computing) plans enjoying special “structural” properties, namely loopy but closed policy structures. Second, we provide an encoding suitable for reactive synthesis that avoids the naive exponential state space blowup. To do so, special care has to be taken to specify the fairness assumption on the environment in a succinct manner.Fil: D'ippolito, Nicolás Roque. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Rodriguez, Natalia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: Sardina, Sebastian. RMIT University; Australi
Banach-Mazur Games with Simple Winning Strategies
We discuss several notions of "simple" winning strategies for
Banach-Mazur games on graphs, such as positional strategies,
move-counting or length-counting strategies, and strategies with a
memory based on finite appearance records (FAR). We investigate
classes of Banach-Mazur games that are determined via these kinds of
winning strategies.
Banach-Mazur games admit stronger determinacy results than classical
graph games. For instance, all Banach-Mazur games with omega-regular
winning conditions are positionally determined. Beyond the
omega-regular winning conditions, we focus here on Muller conditions
with infinitely many colours. We investigate the infinitary Muller
conditions that guarantee positional determinacy for Banach-Mazur
games. Further, we determine classes of such conditions that require
infinite memory but guarantee determinacy via move-counting
strategies, length-counting strategies, and FAR-strategies. We also
discuss the relationships between these different notions of determinacy
Relentful Strategic Reasoning in 1 Alternating-Time Temporal Logic
Temporal logics are a well investigated formalism for the specification, verification, and synthesis of reactive systems.
Within this family, Alternating-Time Temporal Logic (ATL , for short) has been introduced as a useful generalization
of classical linear- and branching-time temporal logics, by allowing temporal operators to be indexed by coalitions of
agents. Classically, temporal logics are memoryless: once a path in the computation tree is quantified at a given node,
the computation that has led to that node is forgotten. Recently, mCTL has been defined as a memoryful variant
of CTL , where path quantification is memoryful. In the context of multi-agent planning, memoryful quantification
enables agents to “relent” and change their goals and strategies depending on their history.
In this paper, we define mATL , a memoryful extension of ATL , in which a formula is satisfied at a certain
node of a path by taking into account both the future and the past. We study the expressive power of mATL ,
its succinctness, as well as related decision problems. We also investigate the relationship between memoryful
quantification and past modalities and show their equivalence. We show that both the memoryful and the past
extensions come without any computational price; indeed, we prove that both the satisfiability and the model-checking
problems are 2EXPTIME-COMPLETE, as they are for AT
Multi-agent Path Planning in Known Dynamic Environments
We consider the problem of planning paths of multiple agents in a dynamic but predictable environment. Typical scenarios are evacuation, reconfiguration, and containment. We present a novel representation of abstract path-planning problems in which the stationary environment is explicitly coded as a graph (called the arena) while the dynamic environment is treated as just another agent. The complexity of planning using this representation is pspace-complete. The arena complexity (i.e., the complexity of the planning problem in which the graph is the only input, in particular, the number of agents is fixed) is np-hard. Thus, we provide structural restrictions that put the arena complexity of the planning problem into ptime(for any fixed number of agents). The importance of our work is that these structural conditions (and hence the complexity results) do not depend on graph-theoretic properties of the arena (such as clique- or tree-width), but rather on the abilities of the agents
The Planning Spectrum - One, Two, Three, Infinity
none2Linear Temporal Logic (LTL) is widely used for defining conditions on the execution paths of dynamic systems. In the case of dynamic systems that allow for nondeterministic evolutions, one has to specify, along with an LTL formula ', which are the paths that are required to satisfy the formula. Two extreme cases are the universal interpretation A.', which requires that the formula be satisfied for all execution paths, and the existential interpretation E.', which requires that the formula be satisfied for some execution path.
When LTL is applied to the definition of goals in planning problems on nondeterministic domains, these two extreme cases are too restrictive. It is often impossible to develop plans that achieve the goal in all the nondeterministic evolutions of a system, and it is too weak to require that the goal is satisfied by some execution.
In this paper we explore alternative interpretations of an LTL formula that are between these extreme cases. We define a new language that permits an arbitrary combination of the A and E quantifiers, thus allowing, for instance, to require that each finite execution can be extended to an execution satisfying an LTL formula (AE.'), or that there is some finite execution whose extensions all satisfy an LTL formula (EA.'). We show that only eight of these combinations of path quantifiers are relevant, corresponding to an alternation of the quantifiers of length one (A and E), two (AE and EA), three (AEA and EAE), and infinity ((AE)! and (EA)!). We also present a planning algorithm for the new language that is based on an automata-theoretic approach, and study its complexity.Marco Pistore; Moshe Y. VardiPistore, Marco; Moshe Y., Vard
The Planning Spectrum - One, Two, Three, Infinity
Linear Temporal Logic (LTL) is widely used for defining conditions on the execution paths of dynamic systems. In the case of dynamic systems that allow for nondeterministic evolutions, one has to specify, along with an LTL formula #, which are the paths that are required to satisfy the formula. Two extreme cases are the universal interpretation A.#, which requires to satisfy the formula for all the possible execution paths, and the existential interpretation E .#, which requires to satisfy the formula for some execution paths