Articles

‘Subsemigroups of virtually free groups: finite Malcev presentations and testing for freeness’

[with E. F. Robertson & N. Ruškuc]

Mathematical Proceedings of the Cambridge Philosophical Society, 141, no. 1 (2006), pp. 57–66.

DOI: 10.1017/s0305004106009236. MR: 2238642. ZBL: 1115.20043.

[ Abstract | Preprint ]

‘Subsemigroups of groups: presentations, Malcev presentations, and automatic structures’

[with E. F. Robertson & N. Ruškuc]

Journal of Group Theory, 9, no. 3 (2006), pp. 397–426.

DOI: 10.1515/jgt.2006.027. MR: 2226621. ZBL: 1151.20044.

[ Abstract | Preprint ]

‘A group-embeddable non-automatic semigroup whose universal group is automatic’

Glasgow Mathematical Journal, 48, no. 2 (2006), pp. 337–342.

DOI: 10.1017/s0017089506003107. MR: 2256982. ZBL: 1108.20056.

[ Abstract | Preprint ]

‘Cancellativity is undecidable for automatic semigroups’

Quarterly Journal of Mathematics, 57, no. 3 (2006), pp. 285–295.

DOI: 10.1093/qmath/hai023. MR: 2253587. ZBL: 1126.20039.

[ Abstract | Preprint | Access on oxfordjournals.org ]

‘Malcev presentations for subsemigroups of groups — a survey’

In C. M. Campbell, M. Quick, E. F. Robertson, & G. C. Smith, eds, Groups St Andrews 2005 (Vol. 1), no. 339 in London Mathematical Society Lecture Note Series, pp. 256–268 (Cambridge: Cambridge University Press, 2007).

MR: 2328165.

[ Abstract | Preprint ]

‘Cancellative and Malcev presentations for finite Rees index subsemigroups and extensions’

[with E. F. Robertson & N. Ruškuc]

Journal of the Australian Mathematical Society, 84, no. 1 (2008), pp. 39–61.

DOI: 10.1017/s1446788708000086. MR: 2469266. ZBL: 1156.20048.

[ Abstract | Preprint ]

‘Automatic presentations for cancellative semigroups’

[with G. Oliver, N. Ruškuc & R. M. Thomas]

In C. Martín-Vide, H. Fernau, & F. Otto, eds, Language and Automata Theory and Applications: Second International Conference, Tarragona, Spain, March 13–19, 2008, no. 5196 in Lecture Notes in Computer Science, pp. 149–159 (Springer, 2008).

DOI: 10.1007/978-3-540-88282-4_15. MR: 2540320. ZBL: 1157.20332.

[ Abstract | Preprint ]

‘Malcev presentations for subsemigroups of direct products of coherent groups’

Journal of Pure and Applied Algebra, 213, no. 6 (2009), pp. 977–990.

DOI: 10.1016/j.jpaa.2008.10.006. MR: 2498789. ZBL: 1178.20050.

[ Abstract | Preprint ]

‘Automaton semigroups’

Theoretical Computer Science, 410, no. 47–49 (2009), pp. 5022–5038.

DOI: 10.1016/j.tcs.2009.07.054. MR: 2583696. ZBL: 1194.68133.

[ Abstract | Preprint ]

‘Automatic presentations for semigroups’

[with G. Oliver, N. Ruškuc & R. M. Thomas]

Information and Computation, 207, no. 11 (2009), pp. 1156–1168.

DOI: 10.1016/j.ic.2009.02.005. MR: 2566948. ZBL: 1192.20040.

[ Abstract | Preprint ]

‘Decision problems for finitely presented and one-relation semigroups and monoids’

[with V. Maltcev]

International Journal of Algebra and Computation, 19, no. 6 (2009), pp. 747–770.

DOI: 10.1142/s0218196709005366. MR: 2572873. ZBL: 1201.20055.

[ Abstract | Preprint ]

‘Monoids presented by rewriting systems and automatic structures for their submonoids’

International Journal of Algebra and Computation, 19, no. 6 (2009), pp. 771–790.

DOI: 10.1142/s0218196709005317. MR: 2572874. ZBL: 1201.20054.

[ Abstract | Preprint ]

‘Automatic semigroups and Bruck–Reilly extensions’

Acta Mathematica Hungarica, 126, no. 1–2 (2010), pp. 1–15.

DOI: 10.1007/s10474-009-8063-8. MR: 2593314.

[ Abstract | Preprint ]

‘Automatic presentations and semigroup constructions’

[with G. Oliver, N. Ruškuc & R. M. Thomas]

Theory of Computing Systems, 47, no. 2 (2010), pp. 568–592.

DOI: 10.1007/s00224-009-9216-4. MR: 2652030. ZBL: 1204.68118.

[ Abstract | Preprint ]

‘Deus ex machina and the aesthetics of proof’

Mathematical Intelligencer, 32, no. 3 (Sept. 2010), pp. 7–11.

DOI: 10.1007/s00283-010-9141-z. MR: 2721302. ZBL: 1247.00009.

[ Abstract | Preprint ]

‘Unary FA-presentable semigroups’

[with N. Ruškuc & R. M. Thomas]

International Journal of Algebra and Computation, 22, no. 4 (2012).

DOI: 10.1142/S0218196712500385.

[ Abstract | Preprint ]

‘Green index in semigroup theory: generators, presentations, and automatic structures’

[with R. Gray & N. Ruškuc]

Semigroup Forum, 85, no. 3 (2012), pp. 448–476.

DOI: 10.1007/s00233-012-9406-2.

[ Abstract | Preprint ]

‘Context-free rewriting systems and word-hyperbolic structures with uniqueness’

[with V. Maltcev]

International Journal of Algebra and Computation, 22, no. 7 (2012).

DOI: 10.1142/S0218196712500610.

[ Abstract | Preprint ]

Forthcoming

‘Hyperbolicity of monoids presented by confluent monadic rewriting systems’

Beiträge zur Algebra und Geometrie, 2013. Forthcoming.

DOI: 10.1007/s13366-012-0116-4.

[ Abstract | Preprint ]

‘Automatic structures for subsemigroups of Baumslag–Solitar semigroups’

Semigroup Forum, 2013. Forthcoming.

arXiv: 1303.1112.

[ Abstract | Preprint ]

Submitted

‘Finite Gröbner–Shirshov bases for Plactic algebras and biautomatic structures for Plactic monoids’

[with R. Gray & A. Malheiro]

Submitted.

arXiv: 1205.4885.

[ Abstract | Preprint ]

‘Automatic Clifford semigroups’

Submitted.

[ Abstract | Preprint ]

‘Markov semigroups, monoids, and groups’

[with V. Maltcev]

Submitted.

arXiv: 1202.3013.

[ Abstract | Preprint ]

‘Finitely presented monoids with linear Dehn function need not have regular cross-sections’

[with V. Maltcev]

Submitted.

arXiv: 1203.0473.

[ Abstract | Preprint ]

‘Subalgebras of FA-presentable algebras’

[with N. Ruškuc]

Submitted.

arXiv: 1206.5548.

[ Abstract | Preprint ]

‘Monoids $\mathrm{Mon}\langle a,b \mid a^\alpha b^\beta a^\gamma b^\delta = b\rangle$ admit finite complete rewriting systems’

[with V. Maltcev]

Submitted.

arXiv: 1302.0982.

[ Abstract ]

‘Unary FA-presentable binary relations: transitivity and classification results’

[with N. Ruškuc]

Submitted.

arXiv: 1303.0214.

[ Abstract | Preprint ]

‘Decision problems for word-hyperbolic semigroups’

Submitted.

arXiv: 1303.1763.

[ Abstract | Preprint ]

In preparation

‘For a few elements more: A survey of finite Rees index’

[with V. Maltcev]

In preparation.

[ Abstract ]

‘Complete rewriting systems and biautomaticity for Chinese and hypoplactic monoids’

[with R. Gray & A. Malheiro]

In preparation.

[ Abstract ]

‘A countable family of congruence-free finitely presented monoids’

[with F. Al-Kharousi, V. Maltcev & A. Umar]

In preparation.

[ Abstract ]