CONTEXT-FREENESS OF THE LANGUAGES OF SCH UTZENBERGER AUTOMATA OF HNN-EXTENSIONS OF FINITE INVERSE SEMIGROUPS

Abstract

We prove that the Schutzenberger graph of any element of the HNN-extension of a fnite inverse semigroup S with respect to its standard presentation is a context-free graph, 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 fnite inverse semigroup S is decidable and lies in the complexity class of polynomial time problems.