Semigroups whith idempotent stabilizers and applications to automata theory - Archive ouverte HAL
Article Dans Une Revue International Journal of Algebra and Computation Année : 1991

Semigroups whith idempotent stabilizers and applications to automata theory

Résumé

We show that every finite semigroup is a quotient of a finite semigroup in which every right stabilizer satisfies the identities x = x^2 and xy = xyx. This result has several consequences. We first give a geometrical application : every finite transformation semigroup has a fixpoint-free covering (a transformation semigroup is fixpoint-free if every element which stabilizes a point is idempotent). Next we use our result and a result of I. Simon on congruences on paths to obtain a purely algebraic proof of a deep theorem of McNaughton on infinite words. Finally, we give an algebraic proof of a theorem of Brown on a finiteness condition for semigroups.

Domaines

Autre [cs.OH]
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Dates et versions

hal-00019824 , version 1 (28-02-2006)

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  • HAL Id : hal-00019824 , version 1

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Bertrand Le Saec, Jean-Eric Pin, Pascal Weil. Semigroups whith idempotent stabilizers and applications to automata theory. International Journal of Algebra and Computation, 1991, 1, pp.291-314. ⟨hal-00019824⟩
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