Multi-linear iterative K-Σ-semialgebras

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 languageEnglish
Pages (from-to)159-170
Number of pages12
JournalElectronic Notes in Theoretical Computer Science
Volume276
Issue number1
DOIs
Publication statusPublished - Sep 29 2011

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Algebra
Semiring
Series
Fixed-point Equation
Trees (mathematics)
Polynomial equation
Coefficient
Linearity
Unique Solution
Polynomials

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.

In: Electronic Notes in Theoretical Computer Science, Vol. 276, No. 1, 29.09.2011, p. 159-170.

Research output: Contribution to journalArticle

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