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INCOMPLETE SEQUENTIAL MACHINES
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1-automaton 2-regular 5-tuple abstract machine automata basic input closed family compatible complete sequential machine congruence relation Consider contradiction defined Definition Denote direct sum disjoint sets distinguished machine equivalence classes equivalence relation Et_i EXAMPLE EXERCISE exists a tape FIGURE finite index finite number finite sets free semigroup given in Fig Hence holds incomplete induction input-distinguished input-equivalent input-output sequences integer isomorphic It+i left cancellation law Lemma machine in Fig minimal-state machine nondeterministic automaton nonempty set Notation ordered pairs output sequence output-empty P2 Pi pi+i positive integer Prove qi+i quasimachine recognition device regular set result right invariant S(pi S(qi satisfy the left semigroup with identity sequential switching circuit set of tapes set union smallest possible number Ss(q ST(q subset Suppose symbol tape of length Theorem Theorem 4.4 two-tape automaton uniform experiment uw+i vw+i X(gi X(pi Xr(g Xs(g