30 citations · 132 across the 31 of their papers we have counts for
5 papers · 1 filter
Subalgebras of FA-presentable algebras
Alan J. Cain, Nik Ruškuc
Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision…
Finite Gröbner--Shirshov bases for Plactic algebras and biautomatic structures for Plactic monoids
Alan J. Cain, Robert D. Gray, António Malheiro
This paper shows that every Plactic algebra of finite rank admits a finite Gröbner--Shirshov basis. The result is proved by using the combinatorial properties of Young tableaux to…
Finitely presented monoids with linear Dehn function need not have regular cross-sections
Alan J. Cain, Victor Maltcev
This paper shows that a finitely presented monoid with linear Dehn function need not have a regular cross-section, strengthening the previously-known result that such a monoid need…
Markov semigroups, monoids, and groups
Alan J. Cain, Victor Maltcev
A group is Markov if it admits a prefix-closed regular language of unique representatives with respect to some generating set, and strongly Markov if it admits such a language of u…
Context-free rewriting systems and word-hyperbolic structures with uniqueness
Alan J. Cain, Victor Maltcev
This paper proves that any monoid presented by a confluent context-free monadic rewriting system is word-hyperbolic. This result then applied to answer a question asked by Duncan &…