Skip to main content
SpringerLink
Log in

Semigroups satisfying x m+n = x n

  • Applications of Conditional Rewriting and New Formalisms
  • Conference paper
  • First Online:
Conditional Term Rewriting Systems (CTRS 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 656))

Included in the following conference series:

Abstract

We summarize recent results on semigroups satisfying the identity x m+n=x n, for n>0 and m>1, and some rewrite techniques that have contributed to their investigation.

This work was supported in part by a Lady Davis fellowship at the Hebrew University and by the U. S. National Science Foundation under Grants CCR-90-07195, CCR-90-24271, and INT-90-16958.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Sergei I. Adian. Classifications of periodic words and their applicaion in group theory. In J. L. Mennicke, editor, Proceedings of a Workshop on Burnside Groups, pages 1–40, Bielefeld, Germany, 1977. Vol. 806 of Lecture Notes in Mathematics, Springer-Verlag, Berlin.

    Google Scholar 

  2. Sergei I. Adian. The Burnside Problem and Identities in Groups. Springer-Verlag, Berlin, 1979. Translated from the Russian.

    Google Scholar 

  3. S. E. Ařson. Proof of the existence of n-valued infinite asymmetric sequences. Matematicheskii Sbornik, 2(44):769–779, 1937.

    Google Scholar 

  4. Leo Bachmair and Nachum Dershowitz. Equational inference, canonical proofs, and proof orderings. J. of the Association for Computing Machinery, 199? To appear. Available as Technical Report DCS-R-92-1746, Department of Computer Science, University of Illinois, Urbana, IL.

    Google Scholar 

  5. Benjamin Benninghofen, Susanne Kemmerich, and Michael M. Richter. Systems of Reductions, volume 277 of Lecture Notes in Computer Science. Springer, Berlin, 1987.

    Google Scholar 

  6. Ronald V. Book. Thue systems as rewriting systems. J. Symbolic Computation, 3(1&2):39–68, February/April 1987.

    Google Scholar 

  7. Janusz Brzozowski. Open problems about regular languages. In R. Book, editor, Formal Language Theory: Perspectives and Open Problems, pages 23–47. Academic Press, New York, 1980.

    Google Scholar 

  8. Janusz Brzozowski, Karl Culik II, and A. Gabrielian. Classification of non-counting events. J. of Computer and System Sciences, 5:41–53, 1971.

    Google Scholar 

  9. W. Burnside. On an unsettled question in the theory of discontinuous groups. Quarterly J. of Pure and Applied Mathematics, 33:230–238, 1902.

    Google Scholar 

  10. Nachum Dershowitz. Rewriting methods for word problems. In M. Ito, editor, Words, Languages & Combinatorics (Proceedings of the International Colloquium, Kyoto, Japan, August 1990), pages 104–118, Singapore, 1992. World Scientific.

    Google Scholar 

  11. Nachum Dershowitz and Jean-Pierre Jouannaud. Rewrite systems. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science B: Formal Methods and Semantics, chapter 6, pages 243–320. North-Holland, Amsterdam, 1990.

    Google Scholar 

  12. Andrzej Ehrenfeucht, David Haussler, and G. Rozenberg. On regularity of context-free languages. Theoretical Computer Science, 27(3):311–332, December 1983.

    Google Scholar 

  13. N. J. Fine and M. S. Wilf. Uniqueness theorems for periodic functions. Proceedings of the American Mathematical Society, 16:109–114, 1965.

    Google Scholar 

  14. J. A. Green and D. Rees. On semigroups in which x r = x. Proceedings of the Cambridge Philosophical Society, 48:35–40, 1952.

    Google Scholar 

  15. M. Hall, Jr. Solution of the Burnside problem for exponent 6. In Proceedings of the National Academy of Sciences of the USA, volume 43, pages 751–753, 1957.

    Google Scholar 

  16. J. M. Howie. An Introduction to Semigroup Theory. Academic Press, London, 1976.

    Google Scholar 

  17. Jieh Hsiang and Michaël Rusinowitch. On word problems in equational theories. In T. Ottmann, editor, Proceedings of the Fourteenth EATCS International Conference on Automata, Languages and Programming, pages 54–71, Karlsruhe, West Germany, July 1987. Vol. 267 of Lecture Notes in Computer Science, Springer-Verlag, Berlin.

    Google Scholar 

  18. Alair Pereira do Lago. On the Burnside semigroups x n = x n+m. In I. Simon, editor, Proceedings of the First Latin American Symposium on Theoretical Informatics, pages 329–343, Sao Paulo, Brazil, April 1992. Vol. 583 of Lecture Notes in Computer Science, Springer-Verlag, Berlin.

    Google Scholar 

  19. Aldo de Luca and Stefano Varricchio. On non counting regular classes. In M. Paterson, editor, Proceedings of the Seventeenth International Colloquium on Automata, Languages and Programming, Warwick, June 1990. EATCS. Vol. 443 of Lecture Notes in Computer Science, Springer-Verlag, Berlin; to appear in Theoretical Computer Science.

    Google Scholar 

  20. Aldo de Luca and Stefano Varricchio. Some regularity conditions based on well quasi-orders. In I. Simon, editor, Proceedings of the First Latin American Symposium on Theoretical Informatics, pages 356–371, Sao Paulo, Brazil, April 1992. Vol. 583 of Lecture Notes in Computer Science, Springer-Verlag, Berlin.

    Google Scholar 

  21. J. McCammond. The solution to the word problem for the relatively free semigroups satisfying t a=ta+b with a≥6. Intl. J. of Algebra and Computation, 1:1–32, 1991.

    Google Scholar 

  22. Thomas E. Nordahl. On the join of the variety of all bands and the variety of all commutative semigroups via conditional rewrite rules. In M. Ito, editor, Words, Languages & Combinatorics (Proceedings of the International Colloquium, Kyoto, Japan, August 1990), pages 365–372, Singapore, 1992. World Scientific.

    Google Scholar 

  23. John Pedersen. Computer solution of word problems in universal algebra. In M. Tangora, editor, Computers in Algebra, pages 103–128. 1988. Vol. 111 of Lecture Notes in Pure and Applied Mathematics, Marcel-Dekker, New York.

    Google Scholar 

  24. John Pedersen. Morphocompletion for one-relation monoids. In N. Dershowitz, editor, Proceedings of the Third International Conference on Rewriting Techniques and Applications, pages 574–578, Chapel Hill, NC, April 1989. Vol. 355 Lecture Notes in Computer Science, Springer, Berlin.

    Google Scholar 

  25. I. N. Sanov. Solution of the Burnside problem for exponent 4. Ucen. Zap. Leningrad Univ., 10:166–170, 1940.

    Google Scholar 

  26. Jorg Siekmann and P. Szabó. A Noetherian and confluent rewrite system for idempotent semigroups. Semigroup Forum, 25(1/2):83–110, 1982.

    Google Scholar 

  27. Craig Squier. Word problems and a homological finiteness condition for monoids. J. of Pure and Applied Algebra, 49:201–217, 1987.

    Google Scholar 

  28. Axel Thue. Über die gegenseitige Lage gleicher Teile gewisser Zeichenreichen. Norske Videnskabssellskabets Skrifter I Mat. Nat. Kl., 1:1–67, 1912.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Illinois, 61801, Urbana, IL, USA

    Nachum Dershowitz

  2. Department of Computer Science, Hebrew University, 91904, Jerusalem, Israel

    Nachum Dershowitz

Authors
  1. Nachum Dershowitz
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Michaël Rusinowitch Jean-Luc Rémy

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dershowitz, N. (1993). Semigroups satisfying x m+n = x n . In: Rusinowitch, M., Rémy, JL. (eds) Conditional Term Rewriting Systems. CTRS 1992. Lecture Notes in Computer Science, vol 656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56393-8_23

Download citation

  • DOI: https://doi.org/10.1007/3-540-56393-8_23

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56393-8

  • Online ISBN: 978-3-540-47549-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation