LATA 2011 (5th conf. Languages and Automata, Theory and Applications)
from 26-05-2011 to 30-05-2011
[en] syntactic monoid ; complexity ; regular language ; numeration system ; decision problem
[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 some well studied problem: decide whether or not a b-recognizable sets of integers is ultimately periodic.