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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 EXAMPLE EXERCISE exists a tape FIGURE finite index finite number finite sets free semigroup function given in Fig Hence holds I2 Pi P2 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 nonempty set Notation ordered pairs output sequence output-empty P2 Pi positive integer quasimachine recognition device regular sets result right invariant S(pi S(qi satisfy the left sequential switching circuit set of tapes set union smallest possible number Ss(p 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