On power series over a graded monoid

Z. Ésik, Werner Kuich

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1 Citation (Scopus)

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.

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Monoid
Power series
Equivalence Problem
Semiring
Coefficient
Non-negative
Finite Type
Integer

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

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title = "On power series over a graded monoid",
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.",
author = "Z. {\'E}sik and Werner Kuich",
year = "2014",
doi = "10.1007/978-3-319-13350-8_4",
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journal = "Lecture Notes in Computer Science",
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publisher = "Springer Verlag",

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AU - Ésik, Z.

AU - Kuich, Werner

PY - 2014

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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.

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JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

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