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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.
Equivalence of automata, finite automata theory, nondeterministic automata, reduction of automata, regular events.

T. Kameda and P. Weiner, "On the State Minimization of Nondeterministic Finite Automata," in IEEE Transactions on Computers, vol. 19, no. , pp. 617-627, 1970.
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