An automata-theoretic approach to branching-time model checking

Kupferman, Orna; Vardi, Moshe Y.; Wolper, Pierre

doi:10.1145/333979.333987

Cited by 412 publications

(359 citation statements)

References 25 publications

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“…The algorithm is based on an automata-theoretic approach (Emerson & Jutla, 1988;Kupferman, Vardi, & Wolper, 2000): planning domains and goals are represented as suitable automata, and planning is reduced to the problem of checking whether a given automaton is nonempty. The proposed algorithm has a time complexity that is doubly exponential in the size of the goal formula.…”

Section: Introductionmentioning

confidence: 99%

The Planning Spectrum - One, Two, Three, Infinity

Pistore¹,

Vardi²

2007

jair

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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 ϕ, which are the paths that are required to satisfy the formula. Two extreme cases are the universal interpretation A.ϕ, which requires that the formula be satisfied for all execution paths, and the existential interpretation E.ϕ, 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.ϕ), or that there is some finite execution whose extensions all satisfy an LTL formula (EA.ϕ). 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) ω and (EA) ω ). We also present a planning algorithm for the new language that is based on an automata-theoretic approach, and study its complexity.

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Section: Introductionmentioning

confidence: 99%

The Planning Spectrum - One, Two, Three, Infinity

Pistore¹,

Vardi²

2007

jair

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“…For sake of space, all other classical concepts of tree, path, set of maximal paths paths(K , w) of a structure K starting in a world w ∈ dom(K ), and unwinding U K w of K in w, are omitted (see [KVW00] for detailed definitions).…”

Section: Preliminariesmentioning

confidence: 99%

Branching-Time Temporal Logics with Minimal Model Quantifiers

Mogavero

Murano

2009

Developments in Language Theory

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Abstract. Temporal logics are a well investigated formalism for the specification and verification of reactive systems. Using formal verification techniques, we can ensure the correctness of a system with respect to its desired behavior (specification), by verifying whether a model of the system satisfies a temporal logic formula modeling the specification. From a practical point of view, a very challenging issue in using temporal logic in formal verification is to come out with techniques that automatically allow to select small critical parts of the system to be successively verified. Another challenging issue is to extend the expressiveness of classical temporal logics, in order to model more complex specifications. In this paper, we address both issues by extending the classical branching-time temporal logic CTL * with minimal model quantifiers (MCTL * ). These quantifiers allow to extract, from a model, minimal submodels on which we check the specification (also given by an MCTL * formula). We show that MCTL * is strictly more expressive than CTL * . Nevertheless, we prove that the model checking problem for MCTL * remains decidable and in particular in PSPACE. Moreover, differently from CTL * , we show that MCTL * does not have the tree model property, is not bisimulation-invariant and is sensible to unwinding. As far as the satisfiability concerns, we prove that MCTL * is highly undecidable. We further investigate the model checking and satisfiability problems for MCTL * sublogics, such as MPML, MCTL, and MCTL + , for which we obtain interesting results. Among the others, we show that MPML retains the finite model property and the decidability of the satisfiability problem.

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“…The universal requirements correspond to conjunctions in the specifications, making the translation of temporal-logic formulas to alternating automata simple and linear [7,18], as opposed to the exponential translation to nondeterministic automata [19]. The linear translation of temporal logic to alternating automata is essential in automata-based algorithms for model checking of branching temporal logic formulas [12], and is useful for further minimization of the automata [16], for handling of incomplete information [11], for algorithms that avoid determinization [10], and more.…”

Section: Introductionmentioning

confidence: 99%

Max and Sum Semantics for Alternating Weighted Automata

Almagor

Kupferman

2011

Automated Technology for Verification and Analysis

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Abstract. In the traditional Boolean setting of formal verification, alternating automata are the key to many algorithms and tools. In this setting, the correspondence between disjunctions/conjunctions in the specification and nondeterministic/universal transitions in the automaton for the specification is straightforward. A recent exciting research direction aims at adding a quality measure to the satisfaction of specifications of reactive systems. The corresponding automata-theoretic framework is based on weighted automata, which map input words to numerical values. In the weighted setting, nondeterminism has a minimum semantics -the weight that an automaton assigns to a word is the cost of the cheapest run on it. For universal branches, researchers have studied a (dual) maximum semantics. We argue that a summation semantics is of interest too, as it captures the intuition that one has to pay for the cost of all conjuncts. We introduce and study alternating weighted automata on finite words in both the max and sum semantics. We study the duality between the min and max semantics, closure under max and sum, the added power of universality and alternation, and arithmetic operations on automata. In particular, we show that universal weighted automata in the sum semantics can represent all polynomials.

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An automata-theoretic approach to branching-time model checking

Cited by 412 publications

References 25 publications

The Planning Spectrum - One, Two, Three, Infinity

The Planning Spectrum - One, Two, Three, Infinity

Branching-Time Temporal Logics with Minimal Model Quantifiers

Max and Sum Semantics for Alternating Weighted Automata

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