On the complexity of omega -automata

Safra, Shmuel

doi:10.1109/sfcs.1988.21948

Cited by 480 publications

(399 citation statements)

References 18 publications

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“…For instance, the universality problem for Büchi automata can be reduced to such games, but the construction that we propose in Section 3 cannot be used. More involved constructionsà la Safra are needed [20].…”

Section: Alg For ω-Regular Gamesmentioning

confidence: 99%

Algorithms for Omega-Regular Games with Imperfect Information

Chatterjee¹,

Doyen²,

Henzinger³

et al. 2007

Logical Methods in Computer Science

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Abstract. We study observation-based strategies for two-player turn-based games on graphs with omega-regular objectives. An observation-based strategy relies on imperfect information about the history of a play, namely, on the past sequence of observations. Such games occur in the synthesis of a controller that does not see the private state of the plant. Our main results are twofold. First, we give a fixed-point algorithm for computing the set of states from which a player can win with a deterministic observation-based strategy for any omega-regular objective. The fixed point is computed in the lattice of antichains of state sets. This algorithm has the advantages of being directed by the objective and of avoiding an explicit subset construction on the game graph. Second, we give an algorithm for computing the set of states from which a player can win with probability 1 with a randomized observation-based strategy for a Büchi objective. This set is of interest because in the absence of perfect information, randomized strategies are more powerful than deterministic ones. We show that our algorithms are optimal by proving matching lower bounds.

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Section: Alg For ω-Regular Gamesmentioning

confidence: 99%

Algorithms for Omega-Regular Games with Imperfect Information

Chatterjee¹,

Doyen²,

Henzinger³

et al. 2007

Logical Methods in Computer Science

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“…In this section we give a short exposition of Safra's determinization [Saf88] and show how to improve it. We replace the constant node names with dynamic names, which allow us to simulate the index appearance record 3 construction within the deterministic automaton.…”

Section: Determinization Of Büchi Automatamentioning

confidence: 99%

“…Safra's Construction. Here we describe Safra's determinization construction [Saf88,Saf89]. The construction takes an NBW and constructs an equivalent DRW.…”

Section: Determinization Of Büchi Automatamentioning

confidence: 99%

“…McNaughton showed a determinization construction that is doubly exponential and results in an automaton with the Muller acceptance condition [McN66]. Safra gives a determinization construction which takes a nondeterministic Büchi automaton with n states and returns a deterministic Rabin automaton with at most (12) n n 2n states and n pairs [Saf88]. An alternative determinization with a similar upper bound that also results in a deterministic Rabin automaton was given by Muller and Schupp [MS95].…”

Section: Introductionmentioning

confidence: 99%

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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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“…Specifically, one can resort to Repeat-Converse-Deterministic PDL (repeat-CDPDL), a variant of PDL that allows for expressing the finiteness of trees and for which satisfiability is EXPTIME-complete [30]. This upper bound, however, is established using sophisticated infinite-tree automata-theoretic techniques (cf., e.g., [24]), which so far have resisted attempts at practically efficient implementation [25,28], due to the use of Safra's determinization construction [23] and parity games [18]. The main advantage of our approach here is that we use only automata on finite trees, which require a much "lighter" automata-theoretic machinery.…”

Section: Proposition 4 ([30]) a 2watamentioning

confidence: 99%

An Automata-Theoretic Approach to Regular XPath

Calvanese

Giacomo

Lenzerini

et al. 2009

Database Programming Languages

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In this paper we present Regular XPath (RXPath), which is a natural extension of XPath with regular expressions over paths that has the same computational properties as XPath: linear-time query evaluation and exponential-time reasoning. To establish these results, we devise a unifying automata-theoretic framework based on two-way weak alternating tree automata. Specifically, we consider automata that have infinite runs on finite trees. This enables us to leverage and simplify existing automata-theoretic machinery and develop algorithms both for query evaluation and for reasoning over queries. With respect to the latter problem, we consider RXPath as a constraint language, and study constraint satisfiability, and query satisfiability and containment under constraints in the setting of RXPath.

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On the complexity of omega -automata

Cited by 480 publications

References 18 publications

Algorithms for Omega-Regular Games with Imperfect Information

Algorithms for Omega-Regular Games with Imperfect Information

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

An Automata-Theoretic Approach to Regular XPath

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