Complexity of Unification in Free Groups and Free Semi-groups

The exponent of periodicity is an important factor in estimates of complexity of word-unification algorithms. We prove 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 our upper bound is almost optimal and exponentially better than the original bound (6n)22n4 + 2. Thus our result implies exponential improvement of known upper bounds on complexity of word-unification algorithms. Moreover we give some evidence that, contrary to the common belief, the algorithm deciding satisfiability of equations in free groups, given by Makanin in not primitive recursive. The proofs are only sketched here. More details will be given in the full version.

• Type: Conference
• Year: 1990
• Where: FOCS
• Authors: Antoni Koscielski, Leszek Pacholski
• Keywords: Exponent, FOCS 1990, Theoretical Computer Science, Upper Bounds, Word-unification Algorithms