On the State Minimization of Nondeterministic Finite Automata

The aim of this paper is to obtain a procedure for finding a minimum state nondeterministic finite automaton (NDA) equivalent to a given (in general, nondeterministic) finite automaton. Given a finite automaton A, we derive from A a matrix of 1´ s and 0´s, called a reduced automaton matrix RAM) of A, in a certain way and show that each state of A corresponds to a grid over the RAM. A grid consists of a set of rows and a set of columns of an RAM such that only 1´s appear at the intersections. It is also shown that the union of all the grids, each of which corresponds to a state of A, covers all the 1 entries of an RAM.