ω-automaton

About: ω-automaton is a research topic. Over the lifetime, 2299 publications have been published within this topic receiving 68468 citations. The topic is also known as: stream automaton & ω-automata.

3-Party message complexity is better than 2-party ones for proving lower bounds on the size of minimal nondeterministic finite automata

Abstract: Despite the facts that automata theory is one of the oldest and most extensively investigated areas of theoretical computer science, and finite automaton is the simplest model of computation, there are still principal open problems about finite automata One of them is to estimate, for a regular language L, the size of the minimal nondeterministic finite automaton accepting L Currently, we do not have any method that would at least assure an approximation of this value, however, a lower bound could be obtained by noticing that the sizes of the minimal deterministic finite automaton and a minimal nondeterministic finite automaton can only be exponentially apart from each other The best known technique for proving lower bound on the size of the minimal nondeterministic finite automata is based on communication and this technique covers all previously used approaches Unfortunately, there exist regular languages with an exponential gap between the communication complexity lower bound and the size of a minimal nondeterministic finite automaton The contribution of this paper is to improve the communication complexity lower bound technique in order to get essentially better lower bounds for some regular languages

Parallel algorithms for finite automata problems

Abstract: Finite automata are among the most extensively studied and understood models of computation. They have wide ranging applications — for example, in image compression, protocol validation, game theory and computational biology — just to mention only some recent ones. Here we will survey efficient parallel algorithms for many fundamental computational problems on finite automata. It is well known that problems involving deterministic finite automata (DFA) have polynomial time algorithms, but the problems become hard when the input automata are nondeterministic (NFA or regular expressions). A similar difference is observed in the case of parallel algorithms: most problems involving DFA as input have NC algorithms, while NC algorithms are unlikely with NFA (or regular expression) as input. In addition to DFA and NFA, we will also consider other inputs such as unambiguous finite automata, regular expressions and prefix grammars.

Separating Exponentially Ambiguous NFA from Polynomially Ambiguous NFA

Abstract: We resolve an open problem raised by Ravikumar and Ibarra on the succinctness of representations relating to the types of ambiguity of finite automata. We show that there exists a family of nondeterministic finite automata {An} over a two-letters alphabet such that, for any positive integer n, An is exponentially ambiguous and has n states, whereas the smallest equivalent deterministic finite automaton has 2n states and any smallest equivalent polynomially ambiguous finite automaton has 2n− 1 states.