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See detailSyntactic complexity of ultimately periodic sets of integers and application to a decision procedure
Lacroix, Anne ULg; Rampersad, Narad; Rigo, Michel ULg et al

in Fundamenta Informaticae (2012), 116

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 ... [more ▼]

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. [less ▲]

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