integer base; syntactic monoid; complexity; ultimately periodic set; decision problem
Abstract :
[en] We compute the cardinality of the syntactic monoid of the language 0* rep_b(mN) made of base b expansions of the multiples of the integer m. We also give lower bounds for the syntactic complexity of any (ultimately) periodic set of integers written in base b. We apply our results to a well studied problem: decide whether or not a b-recognizable set of integers is ultimately periodic.
Disciplines :
Computer science Mathematics
Author, co-author :
Lacroix, Anne ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Rampersad, Narad
Rigo, Michel ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Vandomme, Elise ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
Syntactic complexity of ultimately periodic sets of integers and application to a decision procedure
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