8 citations · 11 across the 7 of their papers we have counts for
5 papers · 1 filter
Context-free word problem semigroups
Tara Brough, Alan J. Cain, Markus Pfeiffer
This paper studies the classes of semigoups and monoids with context-free and deterministic context-free word problem. First, some examples are exhibited to clarify the relationshi…
Two applications of monoid actions to cross-sections
Tara Brough, Alan J. Cain, Victor Maltcev
Using a construction that builds a monoid from a monoid action, this paper exhibits an example of a direct product of monoids that admits a prefix-closed regular cross-section, but…
The monoids of the patience sorting algorithm
Alan J. Cain, António Malheiro, Fábio M. Silva
The left patience sorting (lPS) monoid, also known in the literature as the Bell monoid, and the right patient sorting (rPS) monoid are introduced by defining certain congruences o…
A countable family of finitely presented infinite congruence-free monoids
Alan J. Cain, Victor Maltcev, Abdullahi Umar
We prove that monoids are congruence-free for all . This provides a ne…
Monoids admit finite complete rewriting systems
Alan Cain, Victor Maltcev
We prove that every monoid admits a finite complete rewriting system. Furthermore we prove that $\mathrm{Mon}\langle a,b:ab^2a^2b^2=…