Efficient computation in groups and simplicial complexes

Author:
John C. Stillwell

Journal:
Trans. Amer. Math. Soc. **276** (1983), 715-727

MSC:
Primary 03D15; Secondary 03D40, 20F10, 57M05

DOI:
https://doi.org/10.1090/S0002-9947-1983-0688973-8

MathSciNet review:
688973

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Abstract: Using HNN extensions of the Boone-Britton group, a group is obtained which simulates Turing machine computation in linear space and cubic time. Space in is measured by the length of words, and time by the number of substitutions of defining relators and conjugations by generators required to convert one word to another. The space bound is used to derive a PSPACE-complete problem for a topological model of computation previously used to characterize NP-completeness and RE-completeness.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1983-0688973-8

Keywords:
Word problem for groups,
Turing machines,
two-dimensional complexes,
polynomial time computation

Article copyright:
© Copyright 1983
American Mathematical Society