Bideterministic automata and minimal representations of regular languages

Minimal Nondeterministic Finite Automata and Atoms of Regular Languages

We examine the NFA minimization problem in terms of atomic NFA’s, that is, NFA’s in which the right language of every state is a union of atoms, where the atoms of a regular language are non-empty intersections of complemented and uncomplemented left quotients of the language. We characterize all reduced atomic NFA’s of a given language, that is, those NFA’s that have no equivalent states. Usin...

Regular Languages and Finite Automata

Regular Languages and Finite Automata

In 1943, McCulloch and Pitts [4] published a pioneering work on a model for studying the behavior of the nervous systems. Following up on the ideas of McCulloch and Pitts, Kleene [3] wrote the first paper on finite automata and regular expressions. A finite automaton can be considered as the simplest machine model in that the machine has a finite memory; that is, the memory size is independent ...

Minimal Partial Languages and Automata

Partial words are sequences of characters from an alphabet in which some positions may be marked with a “hole” symbol, . We can create a -substitution mapping this symbol to a subset of the alphabet, so that applying such a substitution to a partial word results in a set of full words (ones without holes). This setup allows us to compress regular languages into smaller partial languages. Determ...

Regular Ideal Languages and Synchronizing Automata

We introduce the notion of reset left regular decomposition of an ideal regular language and we prove that there is a one-to-one correspondence between these decompositions and strongly connected synchronizing automata. We show that each ideal regular language has at least a reset left regular decomposition. As a consequence each ideal regular language is the set of synchronizing words of some ...