Languages, Automata, and Logic

Thomas, Wolfgang

doi:10.1007/978-3-642-59126-6_7

Cited by 733 publications

(615 citation statements)

References 90 publications

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“…Using standard techniques for translating automata to logic (cf. [Tho97]), one describes in WMSO that the corresponding tuple of finite trees is accepted by the automaton.…”

Section: Automatic-like Structuresmentioning

confidence: 99%

Transforming structures by set interpretations

Colcombet¹,

Löding²

2007

Logical Methods in Computer Science

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Abstract. We consider a new kind of interpretation over relational structures: finite sets interpretations. Those interpretations are defined by weak monadic second-order (WMSO) formulas with free set variables. They transform a given structure into a structure with a domain consisting of finite sets of elements of the orignal structure. The definition of these interpretations directly implies that they send structures with a decidable WMSO theory to structures with a decidable first-order theory. In this paper, we investigate the expressive power of such interpretations applied to infinite deterministic trees. The results can be used in the study of automatic and tree-automatic structures.

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“…Using standard techniques for translating automata to logic (cf. [Tho97]), one describes in WMSO that the corresponding tuple of finite trees is accepted by the automaton.…”

Section: Automatic-like Structuresmentioning

confidence: 99%

Transforming structures by set interpretations

Colcombet¹,

Löding²

2007

Logical Methods in Computer Science

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“…We specifically consider reachability, safety, Büchi, coBüchi, and parity objectives, all of them Borel measurable. The parity objectives are a canonical form to express all ω-regular objectives [21]. For a play π = ℓ 0 σ 0 ℓ 1 .…”

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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“…Let us list some fundamental and well-known properties of k-types for any of the logics L above; here we suppress the reference to L for simplicity of notation. The proofs of these facts can be found in several sources, we mention [12,18,19] for MSO and FO, and [13] for FO[<]+MOD.…”

Section: Logical Background and Main Resultsmentioning

confidence: 99%

“…While H supplies information about the infinite occurrence of certain segment types, FO[S]-sentences can only express such occurrences in numbers up to a certain finite bound. Indeed, it is well-known that the FO-theory of M = (N, S, P ) is decidable iff for each isomorphism type τ of finite segments and each m, one can decide whether τ occurs ≥ m times in M (see, e.g., [16,19]). …”

Section: The Successor Theorymentioning

confidence: 99%

Decidable Theories of the Ordering of Natural Numbers with Unary Predicates

Rabinovich

Thomas

2006

Lecture Notes in Computer Science

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Abstract.Expansions of the natural number ordering by unary predicates are studied, using logics which in expressive power are located between first-order and monadic second-order logic. Building on the modeltheoretic composition method of Shelah, we give two characterizations of the decidable theories of this form, in terms of effectiveness conditions on two types of "homogeneous sets". We discuss the significance of these characterizations, show that the first-order theory of successor with extra predicates is not covered by this approach, and indicate how analogous results are obtained in the semigroup theoretic and the automata theoretic framework.

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Languages, Automata, and Logic

Cited by 733 publications

References 90 publications

Transforming structures by set interpretations

Transforming structures by set interpretations

Algorithms for Omega-Regular Games with Imperfect Information

Decidable Theories of the Ordering of Natural Numbers with Unary Predicates

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