Groups whose word problems are not semilinear

References

[1] I. Agol, The virtual Haken conjecture, Doc. Math. 18 (2013), 1045–1087, With an appendix by Agol, Daniel Groves, and Jason Manning. Search in Google Scholar

[2] A. V. Anīsīmov, The group languages, Kibernet. (Kiev) 4 (1971), 18–24. Search in Google Scholar

[3] M. Aschenbrenner, S. Friedl and H. Wilton, 3-manifold Groups, EMS Ser. Lect. Math., European Mathematical Society (EMS), Zürich, 2015. 10.4171/154Search in Google Scholar

[4] G. Baumslag, Lecture Notes on Nilpotent Groups, CBMS Reg. Conf. Ser. Math. 2, American Mathematical Society, Providence, 1971. Search in Google Scholar

[5] G. Baumslag and D. Solitar, Some two-generator one-relator non-Hopfian groups, Bull. Amer. Math. Soc. 68 (1962), 199–201. 10.1090/S0002-9904-1962-10745-9Search in Google Scholar

[6] A. Brandstädt, V. B. Le and J. P. Spinrad, Graph Classes: A Survey, SIAM Monogr. Discrete Math. Appl., Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 1999. 10.1137/1.9780898719796Search in Google Scholar

[7] T. Brough, Groups with poly-context-free word problem, Groups Complex. Cryptol. 6 (2014), no. 1, 9–29. 10.1515/gcc-2014-0002Search in Google Scholar

[8] T. Ceccherini-Silberstein, M. Coornaert, F. Fiorenzi, P. E. Schupp and N. W. M. Touikan, Multipass automata and group word problems, Theoret. Comput. Sci. 600 (2015), 19–33. 10.1016/j.tcs.2015.06.054Search in Google Scholar

[9] M. Dehn, Über unendliche diskontinuierliche Gruppen, Math. Ann. 71 (1911), no. 1, 116–144. 10.1007/BF01456932Search in Google Scholar

[10] W. Dicks and I. J. Leary, Presentations for subgroups of Artin groups, Proc. Amer. Math. Soc. 127 (1999), no. 2, 343–348. 10.1090/S0002-9939-99-04873-XSearch in Google Scholar

[11] V. Diekert and A. Weiß, Context-free groups and their structure trees, Internat. J. Algebra Comput. 23 (2013), no. 3, 611–642. 10.1142/S0218196713500124Search in Google Scholar

[12] M. Elder, A context-free and a 1-counter geodesic language for a Baumslag–Solitar group, Theoret. Comput. Sci. 339 (2005), no. 2–3, 344–371. 10.1016/j.tcs.2005.03.026Search in Google Scholar

[13] R. H. Gilman, Formal languages and infinite groups, Geometric and Computational Perspectives on Infinite Groups (Minneapolis/New Brunswick 1994), DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 25, American Mathematical Society, Providence (1996), 27–51. 10.1090/dimacs/025/03Search in Google Scholar

[14] S. Ginsburg, Algebraic and Automata-theoretic Properties of Formal Languages, North-Holland, Amsterdam, 1975. Search in Google Scholar

[15] F. Haglund and D. T. Wise, Special cube complexes, Geom. Funct. Anal. 17 (2008), no. 5, 1551–1620. 10.1007/s00039-007-0629-4Search in Google Scholar

[16] M. Hall, Jr., The Theory of Groups, The Macmillan, New York, 1959. 10.4159/harvard.9780674592711Search in Google Scholar

[17] M. A. Harrison, Introduction to Formal Language Theory, Addison-Wesley, Reading, 1978. Search in Google Scholar

[18] M.-C. Ho, The word problem of ℤn is a multiple context-free language, Groups Complex. Cryptol. 10 (2018), no. 1, 9–15. Search in Google Scholar

[19] D. F. Holt, M. D. Owens and R. M. Thomas, Groups and semigroups with a one-counter word problem, J. Aust. Math. Soc. 85 (2008), no. 2, 197–209. 10.1017/S1446788708000864Search in Google Scholar

[20] D. F. Holt, S. Rees and C. E. Röver, Groups with context-free conjugacy problems, Internat. J. Algebra Comput. 21 (2011), no. 1–2, 193–216. 10.1142/S0218196711006133Search in Google Scholar

[21] J. E. Hopcroft and J. D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Reading, 1979. Search in Google Scholar

[22] L. Kallmeyer, Parsing Beyond Context-free Grammars, Springer Ser, Cognitive Technol., Springer, Berlin, 2010. 10.1007/978-3-642-14846-0Search in Google Scholar

[23] R. P. Kropholler and D. Spiriano, The class of groups with MCF word problem is closed under free products, preprint (2017). Search in Google Scholar

[24] J. Lehnert and P. Schweitzer, The co-word problem for the Higman–Thompson group is context-free, Bull. Lond. Math. Soc. 39 (2007), no. 2, 235–241. 10.1112/blms/bdl043Search in Google Scholar

[25] A. Mateescu and A. Salomaa, Formal languages: An introduction and a synopsis, Handbook of Formal Languages. Vol. 1, Springer, Berlin (1997), 1–39. 10.1007/978-3-642-59136-5_1Search in Google Scholar

[26] D. E. Muller and P. E. 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

[27] M. Nivat, Transductions des langages de Chomsky, Ann. Inst. Fourier (Grenoble) 18 (1968), no. 1, 339–455. 10.5802/aif.287Search in Google Scholar

[28] A. Y. Ol’shanskii and M. V. Sapir, Length and area functions on groups and quasi-isometric Higman embeddings, Internat. J. Algebra Comput. 11 (2001), no. 2, 137–170. 10.1142/S0218196701000401Search in Google Scholar

[29] D. W. Parkes and R. M. Thomas, Groups with context-free reduced word problem, Comm. Algebra 30 (2002), no. 7, 3143–3156. 10.1081/AGB-120004481Search in Google Scholar

[30] A. Piggott, On groups presented by monadic rewriting systems with generators of finite order, Bull. Aust. Math. Soc. 91 (2015), no. 3, 426–434. 10.1017/S0004972715000015Search in Google Scholar

[31] S. Salvati, MIX is a 2-MCFL and the word problem in ℤ2 is captured by the IO and the OI hierarchies, J. Comput. System Sci. 81 (2015), no. 7, 1252–1277. 10.1016/j.jcss.2015.03.004Search in Google Scholar

[32] 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

[33] H. Servatius, Automorphisms of graph groups, J. Algebra 126 (1989), no. 1, 34–60. 10.1016/0021-8693(89)90319-0Search in Google Scholar

[34] W. P. Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 3, 357–381. 10.1090/S0273-0979-1982-15003-0Search in Google Scholar

[35] W. P. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc. (N. S.) 19 (1988), no. 2, 417–431. 10.1090/S0273-0979-1988-15685-6Search in Google Scholar

[36] K. Vijay-Shanker, D. J. Weir and A. K. Joshi, Characterizing structural descriptions produced by various grammatical formalisms, Proceedings of the 25th Annual Meeting on Association for Computational Linguistics—ACL ’87, Association for Computational Linguistics, Stroudsburg (1987), 104–111. 10.3115/981175.981190Search in Google Scholar

[37] D. T. Wise, Research announcement: the structure of groups with a quasiconvex hierarchy, Electron. Res. Announc. Math. Sci. 16 (2009), 44–55. 10.3934/era.2009.16.44Search in Google Scholar

[38] D. T. Wise, The structure of groups with a quasiconvex hierarchy, Lectures (2011). Search in Google Scholar