Succinct representation of regular languages by boolean automata

Representation of (Left) Ideal Regular Languages by Synchronizing Automata

We follow language theoretic approach to synchronizing automata and Černý’s conjecture initiated in a series of recent papers. We find a precise lower bound for the reset complexity of a principal ideal languages. Also we show a strict connection between principal left ideals and synchronizing automata. We characterize regular languages whose minimal deterministic finite automaton is synchroniz...

Succinct Representation and Leaf Languages

In this paper, we present stronger results in the theory of succinct problem representation and establish a close relationship between succinct problems and leaf languages. As a major tool, we use projection reductions from descriptive complexity theory. A succinct problem is a problem whose high complexity stems from the fact that its instances are not given straightforward, but are themselves...

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 ...

Boolean Circuit Complexity of Regular Languages

In this paper we define a new descriptional complexity measure for Deterministic Finite Automata, BC-complexity, as an alternative to the state complexity. We prove that for two DFAs with the same number of states BC-complexity can differ exponentially. In some cases minimization of DFA can lead to an exponential increase in BC-complexity, on the other hand BC-complexity of DFAs with a large st...