Abstract :
The problem of reducing the number of states in an arbitrary incompletely specified deterministic finite-state machine to k states (for a given k) has proven intractible to solution within "reasonable" time; most techniques seem to require exponential time. Two reduction techniques–state assignment to the DON\´T CARE entries, and so-called "state splitting"–are investigated. For both of the techniques, the question, "Can I achieve an equivalent k state machine?" is shown to be polynomial complete, with the resulting conjecture that neither is solvable in time bounded by a polynomial function of the size of the machine.
Keywords :
DoN´r CARE conditions, fmite automaton, incompletely specified finite-state machine, machine minimization, maximum compatibles, polynomial complete, polynomial reducible, state reduction, state splitting, sequential machine.; Automata; Polynomials; Turing machines; DoN´r CARE conditions, fmite automaton, incompletely specified finite-state machine, machine minimization, maximum compatibles, polynomial complete, polynomial reducible, state reduction, state splitting, sequential machine.;
