Lower Bounds for Complementation of ω-Automata Via the Full Automata Technique

Yan, Qiqi

doi:10.1007/11787006_50

Cited by 42 publications

(59 citation statements)

References 15 publications

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“…This is in contrast with many translations in automata-theory (c.f. [24], as well as our lower bound proof here), where moving to an alphabet of a constant size does not change the state blow-up.…”

Section: Introductionsupporting

confidence: 57%

“…over an alphabet of 8 letters, such that for every n ≥ 4, the UBW U n has n states, and every NBW equivalent to U n has at least 1 6 3 n states. In [24], Yan presents the "full automata approach", suggesting to seek for lower bounds on automata with unbounded alphabets, allowing every possible transition. Only then, should one try to implement the required rich transitions via finite words over a fixed alphabet.…”

Section: Theoremmentioning

confidence: 99%

“…2 This solves negatively the long-standing open problem of improving the breakpoint construction to one with an O(2 n ) blow-up. As in [24], our lower-bound proof starts with automata with an exponential alphabet, which we then encode using a fixed-size alphabet. We show that the Ω(3 n ) lower bound applies also to the determinization of nondeterministic co-Büchi word automata and for alternation removal in alternating Büchi tree automata [18].…”

Section: Introductionmentioning

confidence: 99%

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Alternation Removal in Büchi Automata

Boker

Kupferman

Rosenberg

2010

Automata, Languages and Programming

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Abstract. Alternating automata play a key role in the automata-theoretic approach to specification, verification, and synthesis of reactive systems. Many algorithms on alternating automata, and in particular, their nonemptiness test, involve removal of alternation: a translation of the alternating automaton to an equivalent nondeterministic one. For alternating Büchi automata, the best known translation uses the "breakpoint construction" and involves an O(3 n ) state blowup. The translation was described by Miyano and Hayashi in 1984, and is widely used since, in both theory and practice. Yet, the best known lower bound is only 2 n . In this paper we develop and present a complete picture of the problem of alternation removal in alternating Büchi automata. In the lower bound front, we show that the breakpoint construction captures the accurate essence of alternation removal, and provide a matching Ω(3 n ) lower bound. Our lower bound holds already for universal (rather than alternating) automata with an alphabet of a constant size. In the upper-bound front, we point to a class of alternating Büchi automata for which the breakpoint construction can be replaced by a simpler n2 n construction. Our class, of ordered alternating Büchi automata, strictly contains the class of very-weak alternating automata, for which an n2 n construction is known.

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Section: Introductionsupporting

confidence: 57%

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Alternation Removal in Büchi Automata

Boker

Kupferman

Rosenberg

2010

Automata, Languages and Programming

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“…states [Mic88]. For an NSW with n states and k Streett pairs the best possible DPW has at least (Ω(nk)) n states [Yan06]. We have gotten closer to this lower bound however there is still a large gap between the lower bound and the upper bound.…”

Section: Discussionmentioning

confidence: 79%

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

Piterman¹

2007

Logical Methods in Computer Science

176

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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“…A new complementation construction, which avoids determinization, was introduced in [54], and then tightened in [37] to yield an upper bound of (0.97n) n . On the other hand, Michel's bound was improved in [88] to yield a lower bound to (0.76n) n . Thus, the gap between the lower and upper bound has narrowed, but it is still exponentially wide.…”

Section: Büchi Propertiesmentioning

confidence: 99%

Automata-Theoretic Model Checking Revisited

Vardi

Lecture Notes in Computer Science

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Abstract.In automata-theoretic model checking we compose the design under verification with a Büchi automaton that accepts traces violating the specification. We then use graph algorithms to search for a counterexample trace. The basic theory of this approach was worked out in the 1980s, and the basic algorithms were developed during the 1990s. Both explicit and symbolic implementations, such as SPIN and and SMV, are widely used. It turns out, however, that there are still many gaps in our understanding of the algorithmic issues involved in automata-theoretic model checking. This paper covers the fundamentals of automata-theoretic model checking, reviews recent progress, and outlines areas that require further research.

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Lower Bounds for Complementation of ω-Automata Via the Full Automata Technique

Cited by 42 publications

References 15 publications

Alternation Removal in Büchi Automata

Alternation Removal in Büchi Automata

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

Automata-Theoretic Model Checking Revisited

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