Equational Elements in Additive Algebras

Formal Tree Series

“…A distributive Σ-algebra A, +, 0, Ω is briefly denoted by A if +, 0 and Ω are understood. Similar algebras are considered in Courcelle [15] and Bozapalidis [10].…”

“…The definitions and results on distributive algebras are heavily influenced by Bozapalidis [10], especially by his notion of a K-Γ-algebra. He noticed that the multilinear mappings of his well ω-additive K-Γ-algebras assure that certain important mappings induced by formal power series are continuous.…”

“…He noticed that the multilinear mappings of his well ω-additive K-Γ-algebras assure that certain important mappings induced by formal power series are continuous. (See Theorem 2 of Bozapalidis [10].) We have tried in the forthcoming definition of a distributive algebra to simplify the used type of algebra but to save the important results.…”

“…Formal tree series were introduced by Berstel, Reutenauer [5], and then extensively studied by Bozapalidis [7,8,9,10,11], Bozapalidis, Rahonis [12], Kuich [38,39,40,41,43], Engelfriet, Fülöp, Vogler [19] and Fülöp, Vogler [23].…”

Solving Fixed-Point Equations by Derivation Tree Analysis

“…[Boz99], and, independently, [EKL10]; the essence of the result can be traced back to [BR82,Tha67,CS63]). In other words, the least solution can be obtained by adding the values under V of all its derivation trees.…”