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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 68 (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
On D0L Power Series
 J. UNIV. COMPUT. SCI
, 1997
"... We study D0L power series. We show how elementary morphisms introduced by Ehrenfeucht and Rozenberg can be used in connection with power series, characterize the sequences of rational numbers and integers which can be appear as coefficients in D0L power series and establish various decidability resu ..."
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Cited by 5 (5 self)
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We study D0L power series. We show how elementary morphisms introduced by Ehrenfeucht and Rozenberg can be used in connection with power series, characterize the sequences of rational numbers and integers which can be appear as coefficients in D0L power series and establish various decidability results.
Constantlength substitutions and countable scrambled sets
 Nonlinearity
"... Abstract. In this paper we provide examples of topological dynamical systems having either finite or countable scrambled sets. In particular we study conditions for the existence of LiYorke, asymptotic and distal pairs in constant–length substitution dynamical systems. Starting from a circle rotati ..."
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Cited by 2 (1 self)
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Abstract. In this paper we provide examples of topological dynamical systems having either finite or countable scrambled sets. In particular we study conditions for the existence of LiYorke, asymptotic and distal pairs in constant–length substitution dynamical systems. Starting from a circle rotation we also construct a dynamical system having Li–Yorke pairs, none of which is recurrent. 1.
On the Periodicity of Morphic Words
"... Abstract. Given a morphism h prolongable on a and an integer p, we present an algorithm that calculates which letters occur infinitely often in congruent positions modulo p in the infinite word h ω (a). As a corollary, we show that it is decidable whether a morphic word is ultimately pperiodic. Mor ..."
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Abstract. Given a morphism h prolongable on a and an integer p, we present an algorithm that calculates which letters occur infinitely often in congruent positions modulo p in the infinite word h ω (a). As a corollary, we show that it is decidable whether a morphic word is ultimately pperiodic. Moreover, using our algorithm we can find the smallest similarity relation such that the morphic word is ultimately relationally pperiodic. The problem of deciding whether an automatic sequence is ultimately weakly Rperiodic is also shown to be decidable. Key words: automatic sequence, decidability, morphic word, periodicity, similarity relation 1