Abstract
We propose the study of a wide variety of infinite groups from a computational complexity point of view. We raise some important structural questions on these groups from a computational aspect. The purpose of this paper is to invite the attention of both the theoretical computer science community and the combinatorial group theorists that a fruitful area of cross fertilization may be offering itself. As a specific problem, we consider randomly generated groups and their isomorphism problem.
Research supported by NSF grant CCR-9057486 and a grant from MITL.
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References
G. Baumslag, S.M.Gersten, M.Shapiro, and H. Short. Automatic groups and amalgams, Unpublished.
J.W. Cannon, D.B.A. Epstein, D.F.Holt, M.S.Paterson, and W.P.Thurston, Word processing and group theory, Preprint, University of Warwick, 1990.
J.E.Hopcroft and J.D.Ullman, Introduction to automata theory, languages and computation. Addison Wesley, 1979.
W.Magnus, A. Karrass and D.Solitar, Combinatorial group theory. Interscience Publishers, 1966.
M. Gromov, Hyperbolic groups, in “Essays in group theory”, MSRI series vol 8, S.M.Gersten, editor, Springer Verlag, 1987.
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© 1991 Springer-Verlag Berlin Heidelberg
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Cai, Jy. (1991). Computations over infinite groups. In: Budach, L. (eds) Fundamentals of Computation Theory. FCT 1991. Lecture Notes in Computer Science, vol 529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54458-5_46
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DOI: https://doi.org/10.1007/3-540-54458-5_46
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