Geodesic
Context-Freeness of the Languages of Schützenberger Automata of HNN-Extensions of Finite Inverse Semigroups
Publications de l'Institut Mathématique, _N_S_99 (2016) no. 113, p. 177 .

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We prove that the Schützenberger graph of any element of the HNN-extension of a finite inverse semigroup $S$ with respect to its standard presentation is a context-free graph in the sense of [11], showing that the language $L$ recognized by this automaton is context-free. Finally we explicitly construct the grammar generating $L$, and from this fact we show that the word problem for an HNN-extension of a finite inverse semigroup $S$ is decidable and lies in the complexity class of polynomial time problems.
DOI : 10.2298/PIM141227016A
Classification : 20M18, 20M35, 68Q45
Keywords: inverse semigroup, Schützenberger automaton, context-free language 
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     title = {Context-Freeness of the {Languages} of {Sch\"utzenberger} {Automata} of {HNN-Extensions} of {Finite} {Inverse} {Semigroups}},
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Mohammed Abu Ayyash; Emanuele Rodaro. Context-Freeness of the Languages of Schützenberger Automata of HNN-Extensions of Finite Inverse Semigroups. Publications de l'Institut Mathématique, _N_S_99 (2016) no. 113, p. 177 . doi : 10.2298/PIM141227016A. http://geodesic.mathdoc.fr/articles/10.2298/PIM141227016A/

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