Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-19T14:24:33.977Z Has data issue: false hasContentIssue false
  • English
  • Français

Applying rewriting methods to special monoids

Published online by Cambridge University Press:  24 October 2008

Louxin Zhang
Louxin Zhang
Affiliation:
Department of Computer Science, Faculty of Mathematics, University of Waterloo, CanadaN2L 3G1
Get access Rights & Permissions [Opens in a new window]

Extract

A special monoid is a monoid presented by generators and defining relations of the form w = e, where w is a non-empty word on generators and e is the empty word. Groups are special monoids. But there exist special monoids that are not groups. Special monoids have been extensively studied by Adjan[1] and Makanin[7] (see also [2]).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 3 , November 1992 , pp. 495 - 505
Copyright
Copyright © Cambridge Philosophical Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Adjan, S.. Defining relations and algorithmic problems for groups and semigroups. Proc. Steklov Inst. Math. 85 (1966).Google Scholar
[2]Adjan, S. and Makanin, G.. Investigation on algorithm questions of algebra. Prob. Steklov Inst. Math. 168 (1986). 207–226.Google Scholar
[3]Book, R.. Thue systems as rewriting systems. J. Symbolic Comput. 3 (1987), 39–68.CrossRefGoogle Scholar
[4]Jackson, D.. Some one-relator semigroup presentations with solvable word problems. Math. Proc. Cambridge Philos. Soc. 99 (1986), 433–434.CrossRefGoogle Scholar
[5]Lallament, G.. Semigroups and Combinatorial Applications (Wiley, 1979).Google Scholar
[6]McNaughton, R. and Narendran, P.. Special monoids and special Thue systems. J. Algebra 108 (1987), 248–255.CrossRefGoogle Scholar
[7]Makanin, G.. On the word problem for finitely presented semigroups. Dokl. Akad. Nauk SSSR 171 (1966), 285–287.Google Scholar
[8]Newman, M.. On theories with a combinatorial definition of equivalence. Ann. of Math. 43 (1942), 223–243.CrossRefGoogle Scholar
[9]Otto, F. and Zhang, L.. Decision problems for finite special string-rewriting systems that are confluent on a given congruence class. Ada Inform. 28 (1991), 477–510.Google Scholar
[10]Squier, C.. Units of special and Church-Rosser monoids. Theoret. Comput. Sci. 49 (1987), 13–22.Google Scholar
[11]Zhang, L.. Conjugacy in special monoids. J. Algebra 143 (1991), 487–497.CrossRefGoogle Scholar
[12]Zhang, L.. On the Conjugacy problem for one-relator monoids with nontrivial elements of finite order. Internat. J. Algebra Comput. to appear.Google Scholar