Efficient algorithm for checking multiplicity equivalence for the finite Z - Σ*-automata

  • Authors:

  • Kostyantyn Archangelsky

  • Affiliations:

  • Kiev National University, cybernetics dept, Kiev, Ukraine

  • Venue:
  • DLT'02 Proceedings of the 6th international conference on Developments in language theory
  • Year:
  • 2002

Quantified Score

Hi-index 0.00

Visualization

Abstract

We represent a new fast algorithm for checking multiplicity equivalence for finite Z - Σ* - automata. The classical algorithm of Eilenberg [1]is exponential one. On the other hand, for the finite deterministic automata an analogous Aho - Hopcroft - Ullman [2] algorithm has "almost" linear time complexity. Such a big gap leads to the idea of the existence of an algorithm which is more faster than an exponential one. Hunt and Stearns [3] announced the existence of polynomial algorithm for the Z-Σ* - automata of finite degree of ambiguity only. Tzeng [4] created O(n4) algorithm for the general case. Diekert [5] informed us Tzeng's algorithm can be implemented in O(n3) using traingular matrices. Any way, we propose a new O(n3) algorithm (for the general case). Our algorithm utilizes recent results of Siberian mathematical school (Gerasimov [6], Valitckas [7]) about the structure of rings and does not share common ideas with Eilenberg [1] and Tzeng [4].