Reversible finite automata with halting states (RFA) were first considered by Ambainis and Freivalds to facilitate the research of Kondacs-Watrous quantum finite automata. In this paper we consider some of the algebraic properties of RFA, namely the varieties these automata generate. Consequently, we obtain a characterization of the boolean closure of the classes of languages recognized by thes...

The purpose of the present work is to introduce the concept of bifuzzy core of a fuzzy automaton, which induces a bifuzzy topology on the state-set of this fuzzy automaton. This is shown that this bifuzzy topology can be used to characterize the concepts such as bifuzzy family of submachines, bifuzzy separable family and bifuzzy retrievable family of a fuzzy automaton.

Quantum finite automata (QFAs) are quantum counterparts of the usual finite automata. 1way QFAs recognize the same languages as conventional finite automata but can be exponentially more space-efficient. In this talk, we describe the main results about quantum finite automata and some possible areas for future work. In particular, we will discuss: • the languages for which QFAs can be smaller t...