A survey on fooling sets as effective tools for lower bounds on nondeterministic complexity

Abstract

A fooling set for a regular language is a special set of pairs of strings whose size provides a lower bound on the number of states in any nondeterministic finite automaton accepting this language. We show that, in spite of the fact that the difference between the size of the largest fooling set and the nondeterministic state complexity may be arbitrarily large, the fooling set lower bound methods work in many cases. We modify the method in the case when multiple initial states may save one state. We also state some useful properties that allow us to avoid describing particular fooling sets which may often be difficult and tedious.