Fixed-points and algebras with infinitely long expressions: Part II. μ -clones of regular algebras

Abstract

This paper is a continuation of Tiuryn [16]. The main notion presented in the latter paper is the notion of a regular algebra. As it was proved in Tiuryn [16] for an arbitrary signature Σ the algebra of regular Σ-trees is an initial regular algebra. This means that there are naturally defined “polynomials” for regular algebras, which are determined by infinitely long expressions. The aim of this paper is to investigate this phenomenon.