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INCOMPLETE SEQUENTIAL MACHINES
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2-regular 3-automaton 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 don't-care equivalence classes equivalence relation Et-i Example Exercise exists a tape Figure finite index finite number finite sets free semigroup function given in Fig Hence holds I2 Pi P2 Ik+i 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 Pi positive integer quasimachine recognition device regular sets result right invariant Rk+i S(qi satisfy the left semigroup with identity sequential switching circuit set of tapes set union smallest possible number Ss(q subset Suppose symbol tape of length Theorem Theorem 4.4 two-tape automaton uniform experiment X(pi Xs(p