Automatic Presentations for Cancellative Semigroups. - Alan J. Cain; Graham P. Oliver; Nikola Ruskuc; Richard M. Thomas (LATA, 2008)

Automatic presentations for semigroups. - Alan J. Cain; Graham P. Oliver; Nikola Ruskuc; Richard M. Thomas (Inf. Comput., 2009)

Monoids Presented by Rewriting Systems and Automatic Structures for their Submonoids. - Alan J. Cain (Int. J. Algebra Comput., 2009)

Decision Problems for Finitely Presented and One-Relation Semigroups and Monoids. - Alan J. Cain; Victor Maltcev (Int. J. Algebra Comput., 2009)

Automaton semigroups. - Alan J. Cain (Theor. Comput. Sci., 2009)

Automatic Presentations and Semigroup Constructions. - Alan J. Cain; Graham P. Oliver; Nikola Ruskuc; Richard M. Thomas (Theory Comput. Syst., 2010)

Finitely presented monoids with linear Dehn function need not have regular cross-sections - Alan J. Cain; Victor Maltcev (CoRR, 2012)

Subalgebras of FA-presentable algebras - Alan J. Cain; Nikola Ruskuc (CoRR, 2012)

Context-Free Rewriting Systems and Word-hyperbolic Structures with uniqueness. - Alan J. Cain; Victor Maltcev (Int. J. Algebra Comput., 2012)

Unary FA-Presentable Semigroups. - Alan J. Cain; Nikola Ruskuc; Richard M. Thomas (Int. J. Algebra Comput., 2012)

Automaton semigroup constructions. - Tara Brough; Alan J. Cain (CoRR, 2013)

Decision problems for word-hyperbolic semigroups - Alan J. Cain (CoRR, 2013)

Crystal bases, finite complete rewriting systems, and biautomatic structures for Plactic monoids of types $A_n$, $B_n$, $C_n$, $D_n$, and $G_2$. - Alan J. Cain; Robert D. Gray; António Malheiro (CoRR, 2014)

Markov semigroups, monoids and groups. - Alan J. Cain; Victor Maltcev (Int. J. Algebra Comput., 2014)

Rewriting systems and biautomatic structures for Chinese, hypoplactic, and sylvester monoids. - Alan J. Cain; Robert D. Gray; António Malheiro (Int. J. Algebra Comput., 2015)

Deciding conjugacy in sylvester monoids and other homogeneous monoids. - Alan J. Cain; António Malheiro (Int. J. Algebra Comput., 2015)

Automaton semigroups: new construction results and examples of non-automaton semigroups. - Tara Brough; Alan J. Cain (CoRR, 2016)

Combinatorics of Cyclic Shifts in Plactic, Hypoplactic, Sylvester, and Related Monoids. - Alan J. Cain; António Malheiro (WORDS, 2017)

On finite complete rewriting systems, finite derivation type, and automaticity for homogeneous monoids. - Alan J. Cain; Robert D. Gray; António Malheiro (Inf. Comput., 2017)

Automaton semigroups: New constructions results and examples of non-automaton semigroups. - Tara Brough; Alan J. Cain (Theor. Comput. Sci., 2017)

Identities in Plactic, Hypoplactic, Sylvester, Baxter, and Related Monoids. - Alan J. Cain; António Malheiro (Electron. J. Comb., 2018)

Context-Free Word Problem Semigroups. - Tara Brough; Alan J. Cain; Markus Pfeiffer (DLT, 2019)

Combinatorics of patience sorting monoids. - Alan J. Cain; António Malheiro; Fábio M. Silva (Discret. Math., 2019)

The monoids of the patience sorting algorithm. - Alan J. Cain; António Malheiro; Fábio M. Silva (Int. J. Algebra Comput., 2019)

Crystal monoids & crystal bases: Rewriting systems and biautomatic structures for plactic monoids of types An, Bn, Cn, Dn, and G2. - Alan J. Cain; Robert D. Gray; António Malheiro (J. Comb. Theory A, 2019)

A language hierarchy of binary relations. - Tara Brough; Alan J. Cain (Inf. Comput., 2020)

Reconstructing Young tableaux. - Alan J. Cain; Erkko Lehtonen (J. Comb. Theory A, 2022)

A local characterization of quasi-crystal graphs. - Alan J. Cain; António Malheiro; Fátima Rodrigues 003; Inês Rodrigues (Eur. J. Comb., 2025)