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TitleFactoriality and the pin-reutenauer procedure
Author(s)Almeida, Jorge
Costa, José Carlos
Zeitoun, Marc
Profinite semigroup
Profinite topology
Topological closure
Unary implicit signature
Pure implicit signature
Rational language
Aperiodic semigroup
Burnside pseudovariety
Factorial pseudovariety
Full pseudovariety
Pin-Reutenauer procedure
Issue date15-Mar-2016
PublisherDiscrete Mathematics and Theoretical Computer Science
JournalDiscrete Mathematics and Theoretical Computer Science
Abstract(s)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.
AccessOpen access
Appears in Collections:CMAT - Artigos em revistas com arbitragem / Papers in peer review journals

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