The complexity of tree automata and logics of programs

Emerson, E. Allen; Jutla, Charanjit S.

doi:10.1109/sfcs.1988.21949

Cited by 263 publications

(193 citation statements)

References 24 publications

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“…The tree automaton has a number of states that is doubly exponential and a parity index that is exponential in the length of the formula. A proof of this theorem has been given by Emerson and Jutla (1988).…”

Section: Temporal Logicsmentioning

confidence: 99%

“…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%

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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: Temporal Logicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Planning Spectrum - One, Two, Three, Infinity

Pistore¹,

Vardi²

2007

jair

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“…An exponential time lower time bound follows from the lower bound for PDL in [8], and an exponential time upper time bound was shown in [4].…”

Section: Introductionmentioning

confidence: 94%

“…This was improved later to a quadruply exponential procedure [30]. Finally, combining the techniques in [4] with the techniques in [34] lead to a singly exponential procedure.…”

Section: Introductionmentioning

confidence: 99%

Reasoning about the past with two-way automata

Vardi

1998

Automata, Languages and Programming

243

249

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Abstract. The p-calculus can be viewed as essentially the "ultimate" program logic, as it expressively subsumes all propositional program logics, including dynamic logics, process logics, and temporal logics. It is known that the satisfiability problem for the p-calculus is EXPTIMEcomplete. This upper bound, however, is known for a version of the logic that has only forward modalities, which express weakest preconditions, but not backward modalities, which express strongest postconditions. Our main result in this paper is an exponential time upper bound for the satisfiability problem of the p-calculus with both forward and backward modalities. To get this result we develop a theory of two-way alternating automata on infinite trees.

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“…Solving Rabin games (equivalently, emptiness of nondeterministic Rabin tree automata) is NP-complete in the number of pairs [EJ88]. Solution of parity games is in NP∩co-NP.…”

Section: Determinization Of Büchi and Streett Automatamentioning

confidence: 99%

From Nondeterministic B\"uchi and Streett Automata to Deterministic Parity Automata

Piterman¹

2007

Logical Methods in Computer Science

174

232

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Abstract. In this paper we revisit Safra's determinization constructions for automata on infinite words. We show how to construct deterministic automata with fewer states and, most importantly, parity acceptance conditions. Determinization is used in numerous applications, such as reasoning about tree automata, satisfiability of CTL * , and realizability and synthesis of logical specifications. The upper bounds for all these applications are reduced by using the smaller deterministic automata produced by our construction. In addition, the parity acceptance conditions allows to use more efficient algorithms (when compared to handling Rabin or Streett acceptance conditions).

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The complexity of tree automata and logics of programs

Cited by 263 publications

References 24 publications

The Planning Spectrum - One, Two, Three, Infinity

The Planning Spectrum - One, Two, Three, Infinity

Reasoning about the past with two-way automata

From Nondeterministic B\"uchi and Streett Automata to Deterministic Parity Automata

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