Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-04-30T13:27:02.728Z Has data issue: false hasContentIssue false
  • English
  • Français

Church-Rooser property and homology of monoids

Published online by Cambridge University Press:  04 March 2009

Yves Lafont  and
Alain Prouté
Yves Lafont
Affiliation:
Laboratorie d'Informatique, Ecole Normale Supérieure. (URA 1327 du CNRS)
Alain Prouté
Affiliation:
UFR de Mathématiques, Université de Paris 7. (URA 212 Du CNRS).
Get access Rights & Permissions [Opens in a new window]

Abstract

We present a result of C.C. Squier relating two topics:

— the canonical rewriting systems, which have been widely studied by computer scientists as a tool for solving word problems,

— the homology of groups (more generally of monoids), which belongs to the core of pure mathematics, on the borders of algebra and topology.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 1 , Issue 3 , November 1991 , pp. 297 - 326
Copyright
Copyright © Cambridge University Press 1991

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

Brown, 1982: K. S. Brown. Cohomology of groups. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Burroni, 1991: A. Burroni. Higher-dimensional world problem, to appear in Category Theory and Computer Science, Lecutre Notes in Computer Science.Google Scholar
Greenberg, . 1967: M. Greenberg. Lectures on Algebraic Topology. Benjamin, New York, Amsterdam.Google Scholar
Huet, 1980: G. Huet. Confluent reductions: abstract properties and applications to term rewriting systems. Journal of the ACM 27, 797–821.Google Scholar
Huet-Levy, 1979: G. Huet & J. J. Levy. Call by nedd computations in on-ambiguous linear term rewriting systems. Rapport de Recherche IRIA 359.Google Scholar
Jantzen, 1985: M. Jantzen. A note on a special one-rule semi-Thue system. Inform. Process Lett. 21, 135–140.Google Scholar
Kapur-Narendran, 1985: D. Kapur & P. Narendran. A finite Thue system with decidable word problem and without equivalent finite canonical system. Theor. Comput. Sci. 35, 337–344.Google Scholar
Kobayashi, 1990: Y. Kobayashi. Complete rewritting system and homology of monoid algebras. Journal of pure and Applied Algebra 65, 263–275.Google Scholar
Lang, 1984: S. Lang. Algebra. Addison-Wesley. Reading Massachussets.Google Scholar
LeChenadec, 1986: P. Le Chenadec. Canonical Forms in Finitely Presented Algebras. Pitman, London, John Wiley & Sons, New York, Toronto.Google Scholar
MacLane, 1963: S. Mac Lane. Homology. Springer-Verlag. Berlin.CrossRefGoogle Scholar
McDuff, 1979: D. McDuff. On the classifying spaces of discrete monoids. Topology 18, 313–320.Google Scholar
Spanier, 1966: E. H. Spanier. Algebraic Topolgy. McGraw-Hill, New York.Google Scholar
Squier, 1987: C. C. Squier. World problems and a homological finiteness condition for monoids. Journal of Pure and Applied Algebra 49, 201–217.Google Scholar
Squier-Otto, 1987: C. C. Squier & F. Otto. The word problem for finitely presented monoids and finite canonical rewriting systems, in Jouannaud, J. P. (ed.), Rewriting Techniques and Applications. Lecutre Notes in Computer Science 256, 74–82.Google Scholar
Swan, 1969: R. G. Swan. Groups of cohomological dimension 1, Journal of Algebra 12, 585–601.Google Scholar