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On Power Series over a Graded Monoid

  • Zoltán Ésik
  • Werner KuichEmail author
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8808)

Abstract

We consider power series over a graded monoid \(M\) of finite type. We show first that, under certain conditions, the equivalence problem of power series over \(M\) with coefficients in the semiring \(\mathbb N\) of nonnegative integers can be reduced to the equivalence problem of power series over \(\{x\}^*\) with coefficients in \(\mathbb N\). This result is then applied to rational and recognizable power series over \(M\) with coefficients in \(\mathbb N\), and to rational power series over \(\Sigma ^*\) with coefficients in the semiring \(\mathbb {Q}_+\) of nonnegative rational numbers, where \(\Sigma \) is an alphabet.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.University of SzegedSzegedHungary
  2. 2.Technische Universität WienViennaAustria

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