Results 1  10
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16
Finite automata
 Handbook of Theoretical Computer Science, volume B: Formal Methods and Semantics, chapter 1
, 1990
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Monadic chain logic over iterations and applications to pushdown systems
 In LICS’06
, 2006
"... Logical properties of iterations of relational structures are studied and these decidability results are applied to the model checking of a powerful extension of pushdown systems. It is shown that the monadic chain theory of the iteration of a structure A (in the sense of Shelah and Stupp) is decida ..."
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Logical properties of iterations of relational structures are studied and these decidability results are applied to the model checking of a powerful extension of pushdown systems. It is shown that the monadic chain theory of the iteration of a structure A (in the sense of Shelah and Stupp) is decidable in case the firstorder theory of the structure A is decidable. This result fails if Muchnik’s clonepredicate is added. A model of pushdown automata, where the stack alphabet is given by an arbitrary (possibly infinite) relational structure, is introduced. If the stack structure has a decidable firstorder theory with regular reachability predicates, then the same holds for the configuration graph of this pushdown automaton. This result follows from our decidability result for the monadic chain theory of the iteration. 1.
HIGHLY UNDECIDABLE PROBLEMS FOR INFINITE COMPUTATIONS
 THEORETICAL INFORMATICS AND APPLICATIONS
, 2009
"... We show that many classical decision problems about 1counter ωlanguages, context free ωlanguages, or infinitary rational relations, are Π 1 2complete, hence located at the second level of the analytical hierarchy, and “highly undecidable”. In particular, the universality problem, the inclusion ..."
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We show that many classical decision problems about 1counter ωlanguages, context free ωlanguages, or infinitary rational relations, are Π 1 2complete, hence located at the second level of the analytical hierarchy, and “highly undecidable”. In particular, the universality problem, the inclusion problem, the equivalence problem, the determinizability problem, the complementability problem, and the unambiguity problem are all Π 1 2complete for contextfree ωlanguages or for infinitary rational relations. Topological and arithmetical properties of 1counter ωlanguages, context free ωlanguages, or infinitary rational relations, are also highly undecidable. These very surprising results provide the first examples of highly undecidable problems about the behaviour of very simple finite machines like 1counter automata or 2tape automata.
On the topological complexity of weakly recognizable tree languages
 Proc. FCT 2007, LNCS 4639
, 2007
"... Abstract. We show that the family of tree languages recognized by weak alternating automata is closed by three set theoretic operations that correspond to sum, multiplication by ordinals <ω ω, and pseudoexponentiation with the base ω1 of the Wadge degrees. In consequence, the Wadge hierarchy of weak ..."
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Abstract. We show that the family of tree languages recognized by weak alternating automata is closed by three set theoretic operations that correspond to sum, multiplication by ordinals <ω ω, and pseudoexponentiation with the base ω1 of the Wadge degrees. In consequence, the Wadge hierarchy of weakly recognizable tree languages has the height of at least ε0, that is the least fixed point of the exponentiation with the base ω. 1
On Decidability Properties of OneDimensional Cellular Automata. Equipe de Logique Mathematique
, 2009
"... In a recent paper Sutner proved that the firstorder theory of the phasespace SA = (Q Z, −→) of a onedimensional cellular automaton A whose configurations are elements of Q Z, for a finite set of states Q, and where − → is the “next configuration relation”, is decidable [Sut08b]. He asked whether ..."
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In a recent paper Sutner proved that the firstorder theory of the phasespace SA = (Q Z, −→) of a onedimensional cellular automaton A whose configurations are elements of Q Z, for a finite set of states Q, and where − → is the “next configuration relation”, is decidable [Sut08b]. He asked whether this result could be extended to a more expressive logic. We prove in this paper that this is actuallly the case. We first show that, for each onedimensional cellular automaton A, the phasespace SA is an ωautomatic structure. Then, applying recent results of Kuske and Lohrey on ωautomatic structures, it follows that the firstorder theory, extended with some counting and cardinality quantifiers, of the structure SA, is decidable. We give some examples of new decidable properties for onedimensional cellular automata. In the case of surjective cellular automata, some more efficient algorithms can be deduced from results of [KL08a] on structures of bounded degree. On the other hand we show that the case of cellular automata give new results on automatic graphs. Keywords: Onedimensional cellular automaton; space of configurations; ωautomatic structures; first order theory; cardinality quantifiers; decidability properties; surjective cellular automaton; automatic graph; reachability relation. 1
Borel ranks and Wadge degrees of context free ωlanguages
"... We determine completely the Borel hierarchy of the class of context free ωlanguages, showing that, for each recursive non null ordinal α, there exist some Σ 0 αcomplete and some Π 0 αcomplete ωlanguages accepted by Büchi 1counter automata. ..."
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We determine completely the Borel hierarchy of the class of context free ωlanguages, showing that, for each recursive non null ordinal α, there exist some Σ 0 αcomplete and some Π 0 αcomplete ωlanguages accepted by Büchi 1counter automata.
A Topological Perspective on Diagnosis
, 2008
"... We propose a topological perspective on the diagnosis problem for discreteevent systems. In an infinitary framework, we argue that the construction of a centralized diagnoser is conditioned by two fundamental properties: saturation and openness. We show that these properties are decidable for ωreg ..."
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We propose a topological perspective on the diagnosis problem for discreteevent systems. In an infinitary framework, we argue that the construction of a centralized diagnoser is conditioned by two fundamental properties: saturation and openness. We show that these properties are decidable for ωregular languages. Usually, openness is guaranteed implicitly in practical settings. In contrast to this, we prove that the saturation problem is PSPACEcomplete, which is relevant for the overall complexity of diagnosis.
Highly Undecidable Problems about Recognizability by Tiling Systems
, 2008
"... Altenbernd, Thomas and Wöhrle have considered acceptance of languages of infinite twodimensional words (infinite pictures) by finite tiling systems, with usual acceptance conditions, such as the Büchi and Muller ones, in [1]. It was proved in [9] that it is undecidable whether a Büchirecognizable ..."
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Altenbernd, Thomas and Wöhrle have considered acceptance of languages of infinite twodimensional words (infinite pictures) by finite tiling systems, with usual acceptance conditions, such as the Büchi and Muller ones, in [1]. It was proved in [9] that it is undecidable whether a Büchirecognizable language of infinite pictures is Erecognizable (respectively, Arecognizable). We show here that these two decision problems are actually Π1 2complete, hence located at the second level of the analytical hierarchy, and “highly undecidable”. We give the exact degree of numerous other undecidable problems for Büchirecognizable languages of infinite pictures. In particular, the nonemptiness and the infiniteness problems are Σ1 1complete, and the universality problem, the inclusion problem, the equivalence problem, the determinizability problem, the complementability problem, are all Π1 2complete. It is also Π12complete to determine whether a given Büchi recognizable language of infinite pictures can be accepted row by row using an automaton model over ordinal words of length ω².
Topological Complexity of ContextFreeωLanguages: A Survey
, 2013
"... Abstract. We survey recent results on the topological complexity of contextfree ωlanguages which form the second level of the Chomsky hierarchy of languages of infinite words. In particular, we consider the Borel hierarchy and the Wadge hierarchy of nondeterministic or deterministic contextfreeω ..."
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Abstract. We survey recent results on the topological complexity of contextfree ωlanguages which form the second level of the Chomsky hierarchy of languages of infinite words. In particular, we consider the Borel hierarchy and the Wadge hierarchy of nondeterministic or deterministic contextfreeωlanguages. We study also decision problems, the links with the notions of ambiguity and of degrees of ambiguity, and the special case of ωpowers.
Automata and Formal Languages
, 2003
"... This article provides an introduction to the theory of automata and formal languages. The elements are presented in a historical perspective and the links with other areas are underlined. In particular, applications of the field to linguistics, software design, text processing, computational alg ..."
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This article provides an introduction to the theory of automata and formal languages. The elements are presented in a historical perspective and the links with other areas are underlined. In particular, applications of the field to linguistics, software design, text processing, computational algebra or computational biology are given.