The word problem for finitely presented monoids and finite canonical rewriting systems [chapter]

Craig Squier, Friedrich Otto
1987 Lecture Notes in Computer Science  
The main purpose of this paper is to describe a negative answer to the following question: Does every finitely presented monoid with a decidable word problem have a presentation (~;R) where R is a finite canonical rewriting system? To obtain this answer a certain homological finiteness condition for monoids is considered. If M is a monoid that can be presented by a finite canonical rewriting system, then M is an (FP)3-monoid. Since there are well-known examples of finitely presented groups that
more » ... have easily decidable word problem, but that do not meet this condition, this implies that there are finitely presented monoids (and groups) with decidable word problem that cannot be presented by finite canonical rewriting systems.
doi:10.1007/3-540-17220-3_7 fatcat:7chzcveea5a5feprziyku25vyu