Integer weighted finite automata, matrices, and formal power series over Laurent polynomials

Abstract

It is well known that the family of regular languages (over alphabet A), accepted by finite automata, coincides with the set of supports of the rational and recognizable formal power series over N with the set of variables A. Here we prove that there is a corresponding presentation for languages accepted by integer weighted finite automata, where the weights are from the additive group of integers, via the matrices over Laurent polynomials with integer coefficients. © Springer-Verlag Berlin Heidelberg 2004.