Abstract
The word problem of a group
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-1440140
Funding statement: The material is based upon work supported by the National Science Foundation under Grant no. DMS-1440140 while the author was in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2016 semester.
Acknowledgements
The author would like to thank Robert Gilman for introducing him to this topic, Koji Fujiwara for pointing him to Burago’s lemma, Tullia Dymarz and Moon Duchin for useful discussions and their support, and the anonymous referees for their very useful comments and suggestions.
References
[1] N. Alon and D. B. West, The Borsuk–Ulam theorem and bisection of necklaces, Proc. Amer. Math. Soc. 98 (1986), no. 4, 623–628. 10.1090/S0002-9939-1986-0861764-9Search in Google Scholar
[2] A. V. Anīsīmov, The group languages, Kibernet. (Kiev) (1971), no. 4, 18–24. Search in Google Scholar
[3] K. Borsuk, Drei Sätze über die n-dimensionale euklidische Sphäre, Fund. Math. 20 (1933), no. 1, 177–190. 10.4064/fm-20-1-177-190Search in Google Scholar
[4] D. Y. Burago, Periodic metrics, Representation Theory and Dynamical Systems, Adv. Soviet Math. 9, American Mathematical Society, Providence (1992), 205–210. 10.1090/advsov/009/10Search in Google Scholar
[5] N. Chomsky, Three models for the description of language, IRE Trans. Inform. Theory 2 (1956), no. 3, 113–124. 10.1109/TIT.1956.1056813Search in Google Scholar
[6] J. Dugundji, Topology, Allyn and Bacon, Boston, 1966. Search in Google Scholar
[7] M. Elder, M. Kambites and G. Ostheimer, On groups and counter automata, Internat. J. Algebra Comput. 18 (2008), no. 8, 1345–1364. 10.1142/S0218196708004901Search in Google Scholar
[8] R. H. Gilman, R. P. Kropholler and S. Schleimer, Groups whose word problems are not semilinear, private communication. 10.1515/gcc-2018-0010Search in Google Scholar
[9] R. Gilman and M. Shapiro, On groups whose word problem is solved by a nested stack automaton, preprint (1998), https://arxiv.org/abs/math/9812028. Search in Google Scholar
[10] D. F. Holt, S. Rees and M. Shapiro, Groups that do and do not have growing context-sensitive word problem, Internat. J. Algebra Comput. 18 (2008), no. 7, 1179–1191. 10.1142/S0218196708004834Search in Google Scholar
[11] R. P. Kropholler and D. Spriano, Closure properties in the class of multiple context free groups, preprint (2017), https://arxiv.org/abs/1709.02478. 10.1515/gcc-2019-2004Search in Google Scholar
[12] D. E. Muller and P. E. A. Schupp, Groups, the theory of ends, and context-free languages, J. Comput. System Sci. 26 (1983), no. 3, 295–310. 10.1016/0022-0000(83)90003-XSearch in Google Scholar
[13]
M.-J. Nederhof,
A short proof that
[14] M.-J. Nederhof, Free word order and mcfls, From Semantics to Dialectometry: Festschrift for John Nerbonne, College Publications, London (2017), 273–282. Search in Google Scholar
[15]
S. Salvati,
MIX is a 2-MCFL and the word problem in
[16] H. Seki, T. Matsumura, M. Fujii and T. Kasami, On multiple context-free grammars, Theoret. Comput. Sci. 88 (1991), no. 2, 191–229. 10.1016/0304-3975(91)90374-BSearch in Google Scholar
© 2018 Walter de Gruyter GmbH, Berlin/Boston