3-Party Message Complexity is Better than 2-Party Ones for Proving Lower Bounds on the Size of Minimal Nondeterministic Finite Automata

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 nite 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. 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