Abstract
Let S be the amalgamated free product of two finite inverse semigroups. We prove that the Schutzenberger graph of an element of S with respect to a standard presentation of S is a context-free graph in the sense of Muller and Schupp (Theor. Comput. Sci. 37:51–75, 1985), showing that the language L recognized by the Schutzenberger automaton is context-free. Moreover we construct the grammar generating L proving that L is a deterministic context-free language and we use this fact for solving some algorithmic problems.
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