Simulating alternating tree automata by nondeterministic automata: New results and new proofs of the theorems of Rabin, McNaughton and Safra

Muller, David E.; Schupp, Paul E.

doi:10.1016/0304-3975(94)00214-4

Cited by 173 publications

(118 citation statements)

References 9 publications

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“…The construction is inductive: we begin with building an automaton for the innermost CTL formula [32], and then use projection to encode existential quantification. This requires turning the alternating automata into non-deterministic ones, which comes with an exponential blowup [33]. We apply this procedure recursively, until the last propositional quantifier.…”

Section: B Qctl Model Checking Under the Tree Semanticsmentioning

confidence: 99%

Quantified CTL: Expressiveness and Model Checking

Costa

Laroussinie

Markey

2012

Lecture Notes in Computer Science

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Abstract-While it was defined long ago, the extension of CTL with quantification over atomic propositions has never been studied extensively. Considering two different semantics (depending whether propositional quantification refers to the Kripke structure or to its unwinding tree), we study its expressiveness (showing in particular that QCTL coincides with Monadic Second-Order Logic for both semantics) and characterize the complexity of its model-checking problem, depending on the number of nested propositional quantifiers (showing that the structure semantics populates the polynomial hierarchy while the tree semantics populates the exponential hierarchy). We also show how these results apply to model checking ATL-like temporal logics for games.

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Section: B Qctl Model Checking Under the Tree Semanticsmentioning

confidence: 99%

Quantified CTL: Expressiveness and Model Checking

Costa

Laroussinie

Markey

2012

Lecture Notes in Computer Science

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“…The automaton A ϕ constructed by Theorem 6 can be turned into an equivalent nondeterministic Büchi tree automaton N ϕ [14] with exponentially more states than A ϕ . The language of N ϕ can be restricted to input-preserving transitionsystems (Theorem 3).…”

Section: ⊓ ⊔mentioning

confidence: 99%

“…For such path formulas (and their negations) acceptance of a path can be tested by a deterministic word automaton with three, two, or three states, respectively. The alternating automaton constructed by Theorem 6 is therefore only linear in the length of the specification, and emptiness can be checked (via nondeterminization [14] of this automaton) in time exponential in the length of the specification.…”

Section: ⊓ ⊔mentioning

confidence: 99%

Synthesis for Probabilistic Environments

Schewe

2006

Automated Technology for Verification and Analysis

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Abstract. In synthesis we construct finite state systems from temporal specifications. While this problem is well understood in the classical setting of non-probabilistic synthesis, this paper suggests the novel approach of open synthesis under the assumptions of an environment that chooses its actions randomized rather than nondeterministically. Assuming a randomized environment inspires alternative semantics both for linear-time and branching-time logics. For linear-time, natural acceptance criteria are almost-sure and observable acceptance, where it suffices if the probability measure of accepting paths is 1 and greater than 0, respectively. We distinguish 0-environments, which can freely assign probabilities to each environment action, from ε-environments, where the probabilities assigned by the environment are bound from below by some ε > 0. While the results in case of 0-environments are essentially the same as for nondeterministic environments, the languages occurring in case of ε-environments are topologically different from the results for nondeterministic and 0-environments (in case of LTL, recognizable by weak alternating automata vs. recognizable by deterministic automata). The complexity of open synthesis is, in both cases, EXPTIME and 2EXPTIME-complete for CTL and LTL specifications, respectively.

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“…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]. Michel showed that this is asymptotically optimal and that the best possible upper bound for determinization and complementation is n!…”

Section: Introductionmentioning

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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Simulating alternating tree automata by nondeterministic automata: New results and new proofs of the theorems of Rabin, McNaughton and Safra

Cited by 173 publications

References 9 publications

Quantified CTL: Expressiveness and Model Checking

Quantified CTL: Expressiveness and Model Checking

Synthesis for Probabilistic Environments

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

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