### 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 N of nonnegative integers can be reduced to the equivalence problem of power series over {x}∗with coefficients in N. This result is then applied to rational and recognizable power series over M with coefficients in N, and to rational power series over Σ∗with coefficients in the semiring Q+ of nonnegative rational numbers, where Σ is an alphabet.

Original language | English |
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Pages (from-to) | 49-55 |

Number of pages | 7 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 8808 |

DOIs | |

Publication status | Published - 2014 |

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### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

**On power series over a graded monoid.** / Ésik, Z.; Kuich, Werner.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - On power series over a graded monoid

AU - Ésik, Z.

AU - Kuich, Werner

PY - 2014

Y1 - 2014

N2 - 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 N of nonnegative integers can be reduced to the equivalence problem of power series over {x}∗with coefficients in N. This result is then applied to rational and recognizable power series over M with coefficients in N, and to rational power series over Σ∗with coefficients in the semiring Q+ of nonnegative rational numbers, where Σ is an alphabet.

AB - 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 N of nonnegative integers can be reduced to the equivalence problem of power series over {x}∗with coefficients in N. This result is then applied to rational and recognizable power series over M with coefficients in N, and to rational power series over Σ∗with coefficients in the semiring Q+ of nonnegative rational numbers, where Σ is an alphabet.

UR - http://www.scopus.com/inward/record.url?scp=84916897137&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84916897137&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-13350-8_4

DO - 10.1007/978-3-319-13350-8_4

M3 - Article

AN - SCOPUS:84916897137

VL - 8808

SP - 49

EP - 55

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

SN - 0302-9743

ER -