State Reduction in Incompletely Specified Finite-State Machines

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.