Abstract
Let S be the amalgamated free product of two finite inverse semigroups. We prove that the Schützenberger graph of an element of S with respect to a standard presentation of S is a context-free graph in the sense of Müller and Schupp (Theor. Comput. Sci. 37:51–75, 1985), showing that the language L recognized by the Schützenberger 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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Acknowledgements
The authors are grate to Stuart Margolis for focusing their attention on this problem. Without his suggestion they probably did not pay attention to language theoretical properties of the languages of Schützenberger automata. The third named author acknowledges the support of the Centro de Matemática da Universidade do Porto financed by FCT through the programmes POCTI and POSI, with Portuguese and European Community structural funds and the support of the FCT project SFRH/BPD/65428/2009.
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Communicated by Mark V. Lawson.
This research was done with the partial support of GNSAGA, PRIN “Automi e Linguaggi Formali: aspetti matematici e applicativi” and the ESF project AutoMathA.
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Cherubini, A., Nuccio, C. & Rodaro, E. Amalgams of finite inverse semigroups and deterministic context-free languages. Semigroup Forum 85, 129–146 (2012). https://doi.org/10.1007/s00233-012-9399-x
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DOI: https://doi.org/10.1007/s00233-012-9399-x