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Complexity of unification in free groups and free semi-groups

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2 Author(s)
Koscielski, A. ; Inst. of Comput. Sci., Wroclaw Univ., Poland ; Pacholski, L.

It is proved that the exponent of periodicity of a minimal solution of a word equation is at most 22.54n, where n is the length of the equation. Since the best known lower bound is 20.31n, this upper bound is almost optimal and exponentially better than the original bound. Thus the result implies exponential improvement of known upper bounds on complexity of word-unification algorithms. Evidence is given that, contrary to common belief, the algorithm deciding satisfiability of equations in free groups, given by G.S. Makanin (1977), is not primitive recursive

Published in:

Foundations of Computer Science, 1990. Proceedings., 31st Annual Symposium on

Date of Conference:

22-24 Oct 1990