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Presentations for Subsemigroups of Groups: Ph.D. thesis, University of St Andrews, 2005.
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‘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.
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‘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.
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‘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 ]
‘A note on “Cancellativity is undecidable for automatic semigroups”’: Unpublished note, 2006.
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‘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.
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‘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.
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‘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.
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‘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.
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‘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.
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‘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.
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‘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.
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‘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.
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‘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.
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‘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.
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‘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.
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An annotated translation of Yves Marie André’s Essay on Beauty (1741): (Ebook, 2010).
[ Abstract | Download | Access on archive.org ]
‘Unary FA-presentable semigroups’: [with N. Ruškuc & R. M. Thomas]
International Journal of Algebra and Computation, 22, no. 4 (2012).
DOI: 10.1142/S0218196712500385.
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‘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.
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‘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 ]
‘Monoids $\mathrm{Mon}\langle a,b \mid a^\alpha b^\beta a^\gamma b^\delta a^\varepsilon b^\varphi = b\rangle$ admit finite complete rewriting systems’: [with V. Maltcev]
Technical report. February 2013.
arXiv: 1302.2819.
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