HYPER-MINIMIZING MINIMIZED DETERMINISTIC FINITE STATE AUTOMATA

We present the first (polynomial-time) algorithm for re-ducing a given deterministic finite state automaton (DFA) into a hyper-mini mized DFA, which may have fewer states than the classically min-imized DFA. The price we pay is that the language recognized by thenew machine can differ from the original on a finite number of inputs.These hyper-minimized automata are optimal, in the sense that everyDFA with fewer states must disagree on infinitely many inputs. Withsmall modifications, the construction works also for finite state trans-ducers producing outputs. Within a class of finitely differing languages,the hyper-minimized automaton is not necessarily unique. There mayexist several non-isomorphic machines using the minimum number ofstates, each accepting a separate language finitely-different from theoriginal one. We will show that there are large structural similaritiesamong all these smallest automata