Algebraic Constraints, Automata, and Regular Languages

Algebraic constraints, automata, and regular languages

A class of decision problems is Boolean if it is closed under the set–theoretic operations of union, intersection and complementation. The paper introduces new Boolean classes of decision problems based on algebraic constraints imposed on transitions of finite automata. We discuss issues related to specifications of these classes from algebraic, computational and proof–theoretic points of view.

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 ...

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 ...

Recognizing ω-regular Languages with Probabilistic Automata

Probabilistic finite automata as acceptors for languages over finite words have been studied by many researchers. In this paper, we show how probabilistic automata can serve as acceptors for ω-regular languages. Our main results are that our variant of probabilistic Büchi automata (PBA) is more expressive than non-deterministic ω-automata, but a certain subclass of PBA, called uniform PBA, has ...