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27
Logic and precognizable sets of integers
 Bull. Belg. Math. Soc
, 1994
"... We survey the properties of sets of integers recognizable by automata when they are written in pary expansions. We focus on Cobham’s theorem which characterizes the sets recognizable in different bases p and on its generalization to N m due to Semenov. We detail the remarkable proof recently given ..."
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Cited by 70 (4 self)
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We survey the properties of sets of integers recognizable by automata when they are written in pary expansions. We focus on Cobham’s theorem which characterizes the sets recognizable in different bases p and on its generalization to N m due to Semenov. We detail the remarkable proof recently given by Muchnik for the theorem of CobhamSemenov, the original proof being published in Russian. 1
Finite Presentations of Infinite Structures: Automata and Interpretations
 Theory of Computing Systems
, 2002
"... We study definability problems and algorithmic issues for infinite structures that are finitely presented. After a brief overview over different classes of finitely presentable structures, we focus on structures presented by automata or by modeltheoretic interpretations. ..."
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Cited by 42 (3 self)
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We study definability problems and algorithmic issues for infinite structures that are finitely presented. After a brief overview over different classes of finitely presentable structures, we focus on structures presented by automata or by modeltheoretic interpretations.
Monadic SecondOrder Logic, Graph Coverings and Unfoldings of Transition Systems
"... We prove that every monadic secondorder property of the unfolding of a transition system is a monadic secondorder property of the system itself. An unfolding is an instance of the general notion of graph covering. We consider two more instances of this notion. A similar result is possible for ..."
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Cited by 28 (5 self)
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We prove that every monadic secondorder property of the unfolding of a transition system is a monadic secondorder property of the system itself. An unfolding is an instance of the general notion of graph covering. We consider two more instances of this notion. A similar result is possible for one of them but not for the other.
Monadic Second Order Logic on TreeLike Structures
, 1996
"... An operation M* which constructs from a given structure M a treelike structure whose domain consists of the finite sequences of elements of M is considered. A notion of automata running on such treelike structures is defined. It is shown that automata of this kind characterise expressive power of ..."
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Cited by 21 (6 self)
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An operation M* which constructs from a given structure M a treelike structure whose domain consists of the finite sequences of elements of M is considered. A notion of automata running on such treelike structures is defined. It is shown that automata of this kind characterise expressive power of monadic second order logic (MSOL) over treelike structures. Using this characterisation it is proved that MSOL theory of treelike structures is effectively reducible to that of the original structures. As another application of the characterisation it is shown that MSOL on trees of arbitrary degree is equivalent to first order logic extended with unary least fixpoint operator.
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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Cited by 6 (1 self)
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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.
Logical Theories and Compatible Operations
"... We survey operations on (possibly infinite) relational structures that are compatible with logical theories in the sense that, if we apply the operation to given structures then we can compute the theory of the resulting structure from the theories of the arguments (the logics under consideration fo ..."
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Cited by 5 (1 self)
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We survey operations on (possibly infinite) relational structures that are compatible with logical theories in the sense that, if we apply the operation to given structures then we can compute the theory of the resulting structure from the theories of the arguments (the logics under consideration for the result and the arguments might differ). Besides general compatibility results for these operations we also present several results on restricted classes of structures, and their use for obtaining classes of infinite structures with decidable theories.
Monadic SecondOrder Logic, Graphs and Unfoldings of Transition Systems
 ANNALS OF PURE AND APPLIED LOGIC
, 1995
"... We prove that every monadic secondorder property of the unfolding of a transition system is a monadic secondorder property of the system itself. We prove a similar result for certain graph coverings. ..."
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Cited by 4 (3 self)
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We prove that every monadic secondorder property of the unfolding of a transition system is a monadic secondorder property of the system itself. We prove a similar result for certain graph coverings.
Iterated pushdown automata and sequences of rational numbers
, 2006
"... We introduce a link between automata of level k and treestructures. Thismethod leads to new decidability results about integer sequences. We also reduce some equality problems for sequences of rational numbers to the equivalence problem for deterministic automata of level k. ..."
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Cited by 3 (0 self)
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We introduce a link between automata of level k and treestructures. Thismethod leads to new decidability results about integer sequences. We also reduce some equality problems for sequences of rational numbers to the equivalence problem for deterministic automata of level k.
Rich ωWords and Monadic SecondOrder Arithmetic
 IN: COMPUTER SCIENCE LOGIC, 11TH INTERNATIONAL WORKSHOP, CSL’97, SELECTED PAPERS
, 1998
"... Rich ωwords are onesided infinite strings which have every finite word as a subword (infix). Infixregular ωwords are onesided infinite strings for which the infix set of a suffix is a regular language. We show that for a regular ωlanguage F (a set of predicates definable in B uchi's restr ..."
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Cited by 3 (2 self)
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Rich ωwords are onesided infinite strings which have every finite word as a subword (infix). Infixregular ωwords are onesided infinite strings for which the infix set of a suffix is a regular language. We show that for a regular ωlanguage F (a set of predicates definable in B uchi's restricted monadic second order arithmetic) the following conditions are equivalent: 1. F contains a rich ωword. 2. F is of second Baire category in the Cantor space of ωwords. 3. F is a nonnullset for a class of measures (including the natural Lebesgue measure on Cantor space). 4. F has maximum Hausdorff dimension. This shows that, although we cannot fully translate Compton's result (Theorem 1 below) on rich ZZwords (in the MSO theory of the integers) to MSO arithmetic on naturals, a set definable in MSO arithmetic and containing a rich ωword is large in several respects simultaneously. Moreover, we show under the assumption of an exchanging property for `distinguishing' prefixes that two re...
Model Transformations in Decidability Proofs for Monadic Theories
"... Abstract. We survey two basic techniques for showing that the monadic secondorder theory of a structure is decidable. In the first approach, one deals with finite fragments of the theory (given for example by the restriction to formulas of a certain quantifier rank) and – depending on the fragment ..."
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Abstract. We survey two basic techniques for showing that the monadic secondorder theory of a structure is decidable. In the first approach, one deals with finite fragments of the theory (given for example by the restriction to formulas of a certain quantifier rank) and – depending on the fragment – reduces the model under consideration to a simpler one. In the second approach, one applies a global transformation of models while preserving decidability of the theory. We suggest a combination of these two methods. 1