Abstract
The solvability of the word problem for Yamamura’s HNN-extensions \([S;A_{1},A_{2};\varphi ]\) has been proved in some particular cases. However, we show that, contrary to the group case, the word problem for \([S;A_{1}A_{2};\varphi ]\) is undecidable even if we consider S to have finite \(\mathscr {R}\)-classes, \(A_{1}\) and \(A_{2}\) to be free inverse subsemigroups of finite rank and with zero, and \(\varphi ,\varphi ^{-1}\) to be computable.
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Acknowledgments
The authors acknowledge A. Cherubini for the fruitful discussions and comments. The first author acknowledges support from the Italian Ministry of Foreign Affairs and Bethlehem University through the Italian project E-PLUS, and also acknowledges the PRIN project 2011 “Automi e Linguaggi Formali: Aspetti Matematici e Applicativi”. The second author acknowledges support from the European Regional Development Fund through the programme COMPETE and by the Portuguese Government through the FCT under the project PEst-C/MAT/UI0144/2013 and the support of the FCT project SFRH/BPD/65428/2009.
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Communicated by Mark V. Lawson.
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Ayyash, M.A., Rodaro, E. Undecidability of the word problem for Yamamura’s HNN-extension under nice conditions. Semigroup Forum 93, 86–96 (2016). https://doi.org/10.1007/s00233-015-9750-0
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DOI: https://doi.org/10.1007/s00233-015-9750-0