About the effect of the number of successful paths in an infinite tree on the recognizability by a finite automaton with Buchi conditions

Abstract

We modify an acceptance condition of Büchi automaton on infinite trees: rather than to require that each computation path is successful, we impose various restrictions on the number of successful paths in a run of the automaton on a tree. All these modifications alter the recognizing power of Büchi automata. We examine the classes induced by the acceptance conditions that require ≤α, ≥α, =α successful paths, where α is a cardinal number. It turns out that, except some trivial cases, the “≤” classes are uncomparable with the class Bü of Büchi acceptable tree languages, while the classes “≥” are strictly included in Bü.