Publications

Ph.D. thesis

Presentations for Subsemigroups of Groups: Ph.D. Thesis, University of St Andrews, 2005.
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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 (2006), no. 1, pp. 57–66.
doi: 10.1017/s0305004106009236. MR: 2238642. ZBL: 1115.20043.
[ Abstract | Download preprint ]
‘Subsemigroups of groups: presentations, Malcev presentations, and automatic structures’: [with E. F. Robertson & N. Ruškuc]
Journal of Group Theory 9 (2006), no. 3, pp. 397–426.
doi: 10.1515/jgt.2006.027. MR: 2226621. ZBL: 1151.20044.
[ Abstract | Download preprint ]
‘A group-embeddable non-automatic semigroup whose universal group is automatic’: Glasgow Mathematical Journal 48 (2006), no. 2, pp. 337–342.
doi: 10.1017/s0017089506003107. MR: 2256982. ZBL: 1108.20056.
[ Abstract | Download preprint ]
‘Cancellativity is undecidable for automatic semigroups’: Quarterly Journal of Mathematics 57 (2006), no. 3, pp. 285–295.
doi: 10.1093/qmath/hai023. MR: 2253587. ZBL: 1126.20039.
[ Abstract | Download preprint ]
‘Malcev presentations for subsemigroups of groups — a survey’: in C. M. Campbell, M. Quick, E. F. Robertson & G. C. Smith, editors, Groups St Andrews 2005 (Vol. 1), no. 339 in London Mathematical Society Lecture Note Series, Cambridge University Press, 2007, pp. 256–268. MR: 2328165.
[ Abstract | Download 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 (2008), no. 1, pp. 39–61.
doi: 10.1017/s1446788708000086. MR: 2469266. ZBL: 1156.20048.
[ Abstract | Download preprint ]
‘Automatic presentations for cancellative semigroups’: [with G. Oliver, N. Ruškuc & R. M. Thomas]
in C. Martín-Vide, H. Fernau & F. Otto, editors, Language and Automata Theory and Applications: Second International Conference, Tarragona, Spain, March 13–19, 2008, no. 5196 in Lecture Notes in Computer Science, Springer, 2008, pp. 149–159.
doi: 10.1007/978-3-540-88282-4_15. ZBL: 1157.20332.
[ Abstract | Download preprint ]
‘Malcev presentations for subsemigroups of direct products of coherent groups’: Journal of Pure and Applied Algebra 213 (2009), no. 6, pp. 977–990.
doi: 10.1016/j.jpaa.2008.10.006. MR: 2498789. ZBL: 05534967.
[ Abstract | Download preprint ]
‘Automaton semigroups’: Theoretical Computer Science 410 (2009), no. 47–49, pp. 5022–5038.
doi: 10.1016/j.tcs.2009.07.054. ZBL: 05626970.
[ Abstract | Download preprint ]
‘Automatic presentations for semigroups’: [with G. Oliver, N. Ruškuc & R. M. Thomas]
Information and Computation 207 (2009), no. 11, pp. 1156–1168.
doi: 10.1016/j.ic.2009.02.005.
[ Abstract | Download preprint ]
‘Decision problems for finitely presented and one-relation semigroups and monoids’: [with V. Maltcev]
International Journal of Algebra and Computation 19 (2009), no. 6, pp. 747–770.
doi: 10.1142/s0218196709005366. ZBL: 05627362.
[ Abstract | Download preprint ]
‘Monoids presented by rewriting systems and automatic structures for their submonoids’: International Journal of Algebra and Computation 19 (2009), no. 6, pp. 771–790.
doi: 10.1142/s0218196709005317. ZBL: 05627363.
[ Abstract | Download preprint ]

Technical reports

‘Classification of 2-generated 2-symbol automaton semigroups’: [with V. Maltcev]
CIRCA Technical Report, University of St Andrews. In preparation.
[ Abstract ]

Miscellaneous notes

‘A note on “Cancellativity is undecidable for automatic semigroups”’: 2006. Unrefereed note.
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		Home Contact C.V. Full C.V. Short C.V. Publications All publications Articles Ph.D. thesis Technical reports Miscellaneous notes Seminars & Talks All seminars & talks Conference talks Invited Other Seminars Invited Other Short courses Other talks Mathematics Current research Research collaborators Teaching Previously taught MT3600 Pure Mathematics MT5826 Finite Fields Personal Biography Erdös number Academic ancestry				Ph.D. thesis Presentations for Subsemigroups of Groups Ph.D. Thesis, University of St Andrews, 2005. [ Abstract \| Download ] 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 (2006), no. 1, pp. 57–66. doi: 10.1017/s0305004106009236. MR: 2238642. ZBL: 1115.20043. [ Abstract \| Download preprint ] ‘Subsemigroups of groups: presentations, Malcev presentations, and automatic structures’ [with E. F. Robertson & N. Ruškuc] Journal of Group Theory 9 (2006), no. 3, pp. 397–426. doi: 10.1515/jgt.2006.027. MR: 2226621. ZBL: 1151.20044. [ Abstract \| Download preprint ] ‘A group-embeddable non-automatic semigroup whose universal group is automatic’ Glasgow Mathematical Journal 48 (2006), no. 2, pp. 337–342. doi: 10.1017/s0017089506003107. MR: 2256982. ZBL: 1108.20056. [ Abstract \| Download preprint ] ‘Cancellativity is undecidable for automatic semigroups’ Quarterly Journal of Mathematics 57 (2006), no. 3, pp. 285–295. doi: 10.1093/qmath/hai023. MR: 2253587. ZBL: 1126.20039. [ Abstract \| Download preprint ] ‘Malcev presentations for subsemigroups of groups — a survey’ in C. M. Campbell, M. Quick, E. F. Robertson & G. C. Smith, editors, Groups St Andrews 2005 (Vol. 1), no. 339 in London Mathematical Society Lecture Note Series, Cambridge University Press, 2007, pp. 256–268. MR: 2328165. [ Abstract \| Download 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 (2008), no. 1, pp. 39–61. doi: 10.1017/s1446788708000086. MR: 2469266. ZBL: 1156.20048. [ Abstract \| Download preprint ] ‘Automatic presentations for cancellative semigroups’ [with G. Oliver, N. Ruškuc & R. M. Thomas] in C. Martín-Vide, H. Fernau & F. Otto, editors, Language and Automata Theory and Applications: Second International Conference, Tarragona, Spain, March 13–19, 2008, no. 5196 in Lecture Notes in Computer Science, Springer, 2008, pp. 149–159. doi: 10.1007/978-3-540-88282-4_15. ZBL: 1157.20332. [ Abstract \| Download preprint ] ‘Malcev presentations for subsemigroups of direct products of coherent groups’ Journal of Pure and Applied Algebra 213 (2009), no. 6, pp. 977–990. doi: 10.1016/j.jpaa.2008.10.006. MR: 2498789. ZBL: 05534967. [ Abstract \| Download preprint ] ‘Automaton semigroups’ Theoretical Computer Science 410 (2009), no. 47–49, pp. 5022–5038. doi: 10.1016/j.tcs.2009.07.054. ZBL: 05626970. [ Abstract \| Download preprint ] ‘Automatic presentations for semigroups’ [with G. Oliver, N. Ruškuc & R. M. Thomas] Information and Computation 207 (2009), no. 11, pp. 1156–1168. doi: 10.1016/j.ic.2009.02.005. [ Abstract \| Download preprint ] ‘Decision problems for finitely presented and one-relation semigroups and monoids’ [with V. Maltcev] International Journal of Algebra and Computation 19 (2009), no. 6, pp. 747–770. doi: 10.1142/s0218196709005366. ZBL: 05627362. [ Abstract \| Download preprint ] ‘Monoids presented by rewriting systems and automatic structures for their submonoids’ International Journal of Algebra and Computation 19 (2009), no. 6, pp. 771–790. doi: 10.1142/s0218196709005317. ZBL: 05627363. [ Abstract \| Download preprint ] Forthcoming ‘Automatic presentations and semigroup constructions’ [with G. Oliver, N. Ruškuc & R. M. Thomas] Theory of Computing Systems, 2009. Forthcoming. doi: 10.1007/s00224-009-9216-4. [ Abstract \| Download preprint ] ‘Automatic semigroups and Bruck–Reilly extensions’ Acta Mathematica Hungarica, 2009. Forthcoming. doi: 10.1007/s10474-009-8063-8. [ Abstract \| Download preprint ] ‘Deus ex machina and the aesthetics of proof’ Mathematical Intelligencer, 2009. Forthcoming. [ Abstract \| Download preprint ] Submitted ‘Automatic structures for subsemigroups of Baumslag–Solitar semigroups’ Submitted. [ Abstract \| Download preprint ] ‘Automatic Clifford semigroups’ Submitted. [ Abstract \| Download preprint ] ‘Two concepts of mathematical beauty’ Submitted. [ Abstract ] ‘Green index in semigroup theory: generators, presentations, and automatic structures’ [with R. Gray & N. Ruškuc] Submitted. [ Abstract \| Download preprint ] In preparation ‘The state of automatic semigroups’ [with M. Hoffmann, N. Ruškuc & R. M. Thomas] In preparation. [ Abstract ] ‘Translator automata and applications to the local automatism of certain semigroups’ In preparation. [ Abstract ] ‘L-presentations for semigroups’ In preparation. [ Abstract ] Technical reports ‘Classification of 2-generated 2-symbol automaton semigroups’ [with V. Maltcev] CIRCA Technical Report, University of St Andrews. In preparation. [ Abstract ] Miscellaneous notes ‘A note on “Cancellativity is undecidable for automatic semigroups”’ 2006. Unrefereed note. [ Abstract \| Download ]



		A. J. Cain > Publications

				Colophon	© 1998–2009 A. J. Cain

Publications

Ph.D. thesis

Articles

Forthcoming

Submitted

In preparation

Technical reports

Miscellaneous notes