2011/02/15 by Zoltán Ésik, Esik, Zoltan
Computer Science · Mathematics · #08A70 #68Q70 #Advanced Topics in Algebra #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Logic, programming, and type systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1102.3106
openalex publication_date 2011/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.