J. Almeida ; J. C. Costa ; M. Zeitoun - Factoriality and the Pin-Reutenauer procedure

dmtcs:650 - Discrete Mathematics & Theoretical Computer Science, March 15, 2016, Vol. 18 no. 3 - https://doi.org/10.46298/dmtcs.650
Factoriality and the Pin-Reutenauer procedure

Authors: J. Almeida ; J. C. Costa ; M. Zeitoun

We consider implicit signatures over finite semigroups determined by sets of pseudonatural numbers. We prove that, under relatively simple hypotheses on a pseudovariety V of semigroups, the finitely generated free algebra for the largest such signature is closed under taking factors within the free pro-V semigroup on the same set of generators. Furthermore, we show that the natural analogue of the Pin-Reutenauer descriptive procedure for the closure of a rational language in the free group with respect to the profinite topology holds for the pseudovariety of all finite semigroups. As an application, we establish that a pseudovariety enjoys this property if and only if it is full.

Volume: Vol. 18 no. 3
Section: Automata, Logic and Semantics
Published on: March 15, 2016
Submitted on: March 15, 2016
Keywords: Mathematics - Group Theory,Primary 20M07, Secondary 20M05, 20M35, 68Q70


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