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December 1973 (vol. 22 no. 12)
pp. 1099-1102
C.P. Pfleeger, Department of Computer Science, Pennsylvania State University
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.
Index Terms:
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.
C.P. Pfleeger, "State Reduction in Incompletely Specified Finite-State Machines," IEEE Transactions on Computers, vol. 22, no. 12, pp. 1099-1102, Dec. 1973, doi:10.1109/T-C.1973.223655
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