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Symbolic Dynamics and Finite Automata
, 1999
"... this paper, based on notes by R. Beals and M. Spivak, methods of nite semigroups were introduced to obtain some of the results of G. Hedlund. ..."
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Cited by 26 (9 self)
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this paper, based on notes by R. Beals and M. Spivak, methods of nite semigroups were introduced to obtain some of the results of G. Hedlund.
Forbidden Words in Symbolic Dynamics
, 1999
"... We introduce an equivalence relation ' between functions from N to N. By describing a symbolic dynamical system in terms of forbidden words, we prove that the 'equivalence class of the function that counts the minimal forbidden words of a system is a topological invariant of the syste ..."
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Cited by 19 (8 self)
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We introduce an equivalence relation ' between functions from N to N. By describing a symbolic dynamical system in terms of forbidden words, we prove that the 'equivalence class of the function that counts the minimal forbidden words of a system is a topological invariant of the system. We show that the new invariant is independent from previous ones, but it is not characteristic. In the case of soc systems we prove that the 'equivalence of the corresponding functions is a decidable question. As a more special application, we show, by using the new invariant, that two systems associated to Sturmian words having \dierent slope" are not conjugate. Classication: Symbolic Dynamics, Combinatoric on words, Automata and Formal Languages. 1 Introduction In this paper we present a new topological invariant for Symbolic Dynamics. The techniques we use and some complementary results are from Combinatorics on words and from the theory of Automata and Formal Languages. Indeed there...
Minimal Forbidden Words and Symbolic Dynamics
, 1996
"... . We introduce a new complexity measure of a factorial formal language L: the growth rate of the set of minimal forbidden words. We prove some combinatorial properties of minimal forbidden words. As main result we prove that the growth rate of the set of minimal forbidden words for L is a topolo ..."
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Cited by 4 (1 self)
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. We introduce a new complexity measure of a factorial formal language L: the growth rate of the set of minimal forbidden words. We prove some combinatorial properties of minimal forbidden words. As main result we prove that the growth rate of the set of minimal forbidden words for L is a topological invariant of the dynamical system defined by L. Classification: Automata and Formal Languages 1 Introduction Let L ae A be a factorial language, i.e. a language containing all factors of its words. A word w 2 A is a minimal forbidden word for L if w = 2 L and all proper factors of w belong to L. We denote by MF (L) the language of minimal forbidden words for L. It turns out (as also stressed by the results of this paper) that the combinatorial properties of MF (L) provide an usefull tool to investigate the structure of the language L or of the system that it describes. Consider, for instance, the case of locally testable factorial languages (cf [14]): they are characterized by th...