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Integer Weighted Finite Automata, Matrices and Formal Power Series over Laurent Polynomials

Vesa Halava, Integer Weighted Finite Automata, Matrices and Formal Power Series over Laurent Polynomials. In: H. Maurer G. Paun G. Rozenberg J. karhumäki (Ed.), Theory is Forever, Essays Dedicated to Arto Salomaa on the Occasion of His 70th Birthday, Lecture Notes in Computer Science 3113, 81–88, Springer, 2004.

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 natural numbers 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.

BibTeX entry:

@INBOOK{cHalava04a,
  title = {Integer Weighted Finite Automata, Matrices and Formal Power Series over Laurent Polynomials},
  booktitle = {Theory is Forever, Essays Dedicated to Arto Salomaa on the Occasion of His 70th Birthday},
  author = {Halava, Vesa},
  volume = {3113},
  series = {Lecture Notes in Computer Science},
  editor = {J. karhumäki, H. Maurer G. Paun G. Rozenberg},
  publisher = {Springer},
  pages = {81–88},
  year = {2004},
  keywords = {integer weighted finite automata, formal power series, matrices, Laurent polynomial },
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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