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Remarks concerning finitely generated semigroups having regular sets of unique normal forms

Part of: Special aspects of infinite or finite groups Semigroups

Published online by Cambridge University Press:  09 April 2009

Andrew Cutting  and
Andrew Solomon
Andrew Cutting
Affiliation:
Mathematical Institute University of St AndrewsFife, KY 16 9SSScotland e-mail: [email protected]
Andrew Solomon
Affiliation:
Department of Mathematics and Statistics Simon Fraser UniversityBurnaby, British Columbia VA5 1S6Canada e-mail: [email protected]
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Abstract

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Properties such as automaticity, growth and decidability are investigated for the class of finitely generated semigroups which have regular sets of unique normal forms. Knowledge obtained is then applied to the task of demonstrating that a class of semigroups derived from free inverse semigroups under certain closure operations is not automatic.

MSC classification

Secondary: 20M18: Inverse semigroups 20M05: Free semigroups, generators and relations, word problems 20F10: Word problems, other decision problems, connections with logic and automata
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 70 , Issue 3 , June 2001 , pp. 293 - 310
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Adjan, S. I., ‘On algorithmic problems in effectively complete classes of groups’, Dokl. Akad. Nauk SSSR 123 (1958), 13–16 (in Russian).Google Scholar
[2]Campbell, C. M., Robertson, E. F., Ruškuc, N. and Thomas, R. M., ‘Automatic semigroups’, Theoret. Comput. Sci. (to appear).Google Scholar
[3]Cannon, J. W., Epstein, D. B. A., Holt, D. F., Levy, S. V. F., Paterson, M. S. and Thurston, W. P., Word processing in groups (Jones and Bartlett Publishers, Boston, Massachusetts, 1992).Google Scholar
[4]Duncan, A. J., Robertson, E. F. and Ruškuc, N., ‘Automatic monoids and change of generators’, Math. Proc. Cambridge Philos. Soc. 127 (1999), 403–409.CrossRefGoogle Scholar
[5]Gilman, R., ‘Groups with a rational cross-section’, in: Combinatorial group theory and topology (eds. Gersten, S. M. and Stallings, J. R.) (Princeton University Press, Princeton, New Jersey, 1987) pp. 175–183.CrossRefGoogle Scholar
[6]Hopcroft, J. E. and Ullman, J. D., Introduction to automata theory, languages and computation (Addison-Wesley, Reading, 1979).Google Scholar
[7]Lau, J., ‘Degree of growth of some inverse semigroups’, J. Algebra 204 (1998), 426–439.CrossRefGoogle Scholar
[8]Markov, A., ‘On the impossibility of certain algorithms in the theory of associative systems’, Dokl. Akad. Nauk SSSR 55 (1947), 583–586.Google Scholar
[9]Markov, A., ‘Impossibility of algorithms for recognizing some properties of associative systems’, Dokl. Akad. Nauk SSSR 77 (1951), 953–956.Google Scholar
[10]Petrich, M., Inverse semigroups, Pure and Applied Mathematics (John Wiley and Sons, New York, 1984).Google Scholar
[11]Rabin, M. O., ‘Recursive unsolvability of group theoretic problems’, Ann. of Math. 67 (1958), 172–194.CrossRefGoogle Scholar
[12]Schneerson, L. M. and Easdown, D., ‘Growth and existence of identities in a class of finitely presented inverse semigroups with zero’, Internat. J. Algebra Comput. 6 (1996), 105–121.CrossRefGoogle Scholar
[13]Sims, C. C., Computation with finitely presented groups, Encyclopedia Math. Appl. 48 (Cambridge University Press, Cambridge, 1994).CrossRefGoogle Scholar
[14]Thomas, R., ‘Groups and formal languages’, Lecture at CGAMA, Heriot-Watt, 07 1998.Google Scholar
[15]Ufnarovskij, V. A., Combinatorial and asymptotic methods in algebra, Encyclopedia Math. Sci. 57 (Springer, Berlin, 1995).Google Scholar
[16]Yamamura, A., ‘HNN extensions of inverse semigroups and applications’, Internat. J. Algebra Comput. 7 (1997), 605–624.CrossRefGoogle Scholar