Safraless Decision Procedures

Kupferman, Orna; Vardi, Moshe Y.

doi:10.1109/sfcs.2005.66

Cited by 158 publications

(192 citation statements)

References 24 publications

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“…For larger AE-LTL goals, a doubly exponential time complexity may not be feasible, but it should be noted that this is worst-case complexity. We also note that improved algorithms for plan synthesis is an active research area, including the analysis of simpler LTL goals (Alur & La Torre, 2004) and the development of improved automata-theoretic algorithms (Kupferman & Vardi, 2005).…”

Section: Related Work and Concluding Remarksmentioning

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: Related Work and Concluding Remarksmentioning

confidence: 99%

The Planning Spectrum - One, Two, Three, Infinity

Pistore¹,

Vardi²

2007

jair

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“…Such a translation is part of several decision procedures for LTL (e.g., synthesis and control [PR89]), algorithms for translating LTL to other logics (e.g., LTL to alternation-free µ-calculus [KV05a] and to general µ-calculus [Dam94]), as well as decision procedures for other logics (e.g., satisfiability for CTL * [ES84]). The blow-up that the translation involves plays a role even in algorithms that avoid determinization [KV05b,Kup06].…”

Section: Introductionmentioning

confidence: 99%

The Blow-Up in Translating LTL to Deterministic Automata

Kupferman

Rosenberg

2011

Model Checking and Artificial Intelligence

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Abstract. The translation of LTL formulas to nondeterministic automata involves an exponential blow-up, and so does the translation of nondeterministic automata to deterministic ones. This yields a 2 2 O(n) upper bound for the translation of LTL to deterministic automata. A lower bound for the translation was studied in [KV05a], which describes a 2 2 Ω( √ n) lower bound, leaving the problem of the exact blow-up open. In this paper we solve this problem and tighten the lower bound to 2 2 Ω(n) .

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“…Our upper bound improves the best known upper bound in numerous applications, such as solving games, complementation of tree automata, emptiness of alternating tree automata, satisfiability of µ-calculus with backward modalities and CTL * . In particular, in the recent emptiness algorithm for alternating parity tree automata [KV05] the upper bound is reduced from (12) n 2 n 4n 2 +2n (n!) n to (2n n n!)…”

Section: Discussionmentioning

confidence: 99%

“…Recently, Kupferman and Vardi showed that they can check the emptiness of an alternating parity tree automaton without directly using Safra's determinization [KV05]. Their construction can be used for many game / tree automata applications that require determinization.…”

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

175

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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Safraless Decision Procedures

Cited by 158 publications

References 24 publications

The Planning Spectrum - One, Two, Three, Infinity

The Planning Spectrum - One, Two, Three, Infinity

The Blow-Up in Translating LTL to Deterministic Automata

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

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