### Abstract

We consider K-semialgebras for a commutative semiring K that are at the same time Σ-algebras and satisfy certain linearity conditions. When each finite system of guarded polynomial fixed point equations has a unique solution over such an algebra, then we call it an iterative multi-linear K-Σ-semialgebra. Examples of such algebras include the algebras of Σ-tree series over an alphabet A with coefficients in K, and the algebra of all rational tree series. We show that for many commutative semirings K, the rational Σ-tree series over A with coefficients in K form the free multi-linear iterative K-Σ-semialgebra on A.

Original language | English |
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Pages (from-to) | 159-170 |

Number of pages | 12 |

Journal | Electronic Notes in Theoretical Computer Science |

Volume | 276 |

Issue number | 1 |

DOIs | |

Publication status | Published - Sep 29 2011 |

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### Keywords

- Σ-algebra
- free algebra
- rational tree-series
- Semialgebra
- unique fixed points

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

**Multi-linear iterative K-Σ-semialgebras.** / Ésik, Z.

Research output: Contribution to journal › Article

*Electronic Notes in Theoretical Computer Science*, vol. 276, no. 1, pp. 159-170. https://doi.org/10.1016/j.entcs.2011.09.020

}

TY - JOUR

T1 - Multi-linear iterative K-Σ-semialgebras

AU - Ésik, Z.

PY - 2011/9/29

Y1 - 2011/9/29

N2 - We consider K-semialgebras for a commutative semiring K that are at the same time Σ-algebras and satisfy certain linearity conditions. When each finite system of guarded polynomial fixed point equations has a unique solution over such an algebra, then we call it an iterative multi-linear K-Σ-semialgebra. Examples of such algebras include the algebras of Σ-tree series over an alphabet A with coefficients in K, and the algebra of all rational tree series. We show that for many commutative semirings K, the rational Σ-tree series over A with coefficients in K form the free multi-linear iterative K-Σ-semialgebra on A.

AB - We consider K-semialgebras for a commutative semiring K that are at the same time Σ-algebras and satisfy certain linearity conditions. When each finite system of guarded polynomial fixed point equations has a unique solution over such an algebra, then we call it an iterative multi-linear K-Σ-semialgebra. Examples of such algebras include the algebras of Σ-tree series over an alphabet A with coefficients in K, and the algebra of all rational tree series. We show that for many commutative semirings K, the rational Σ-tree series over A with coefficients in K form the free multi-linear iterative K-Σ-semialgebra on A.

KW - Σ-algebra

KW - free algebra

KW - rational tree-series

KW - Semialgebra

KW - unique fixed points

UR - http://www.scopus.com/inward/record.url?scp=80054953447&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80054953447&partnerID=8YFLogxK

U2 - 10.1016/j.entcs.2011.09.020

DO - 10.1016/j.entcs.2011.09.020

M3 - Article

AN - SCOPUS:80054953447

VL - 276

SP - 159

EP - 170

JO - Electronic Notes in Theoretical Computer Science

JF - Electronic Notes in Theoretical Computer Science

SN - 1571-0661

IS - 1

ER -