Deterministic finite H-Automata and ω-regular partial languages

Partial words, that is, finite words with holes, were introduced in the 70s by Fischer and Paterson, with respect to bioinformatics applications. Infinite partial words were introduced later. Recently, Dassow et al.’s connected partial words and regular languages. In this paper, we extend the local partial languages to local ω-partial languages and study their closure properties. We introduce the subclass of ω-regular partial languages called Büchi local ω-partial languages and we define deterministic finite H-automaton with acceptance condition on ω-partial words and deterministic finite H-local automaton. Further, we establish relationships between deterministic finite H-local automaton, local ω-partial languages and Büchi local ω-partial languages. Finally, we show that every ω-regular partial languages is a projection of a Büchi local ω-partial languages.