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Recognizers RabinScott Automata
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A/tt admissible decomposition admissible partition algebra automata axioms belong blocks of tt called computation congruence relation considered construction corresponding coset of H cyclic group defined definition denoted direct product elements of G equations equivalence relation example exists finite index finite number following theorem forms a subsemigroup free regular set free semigroup graph G group G group isomorphic grouplike semiautomaton groupoid G hence homomorphic image idempotent identity implies integers Lemma maton monoid multiplication noncounting regular set nondeterministic normal subgroup Notice number of elements obtained one-to-one mapping output-consistent pairs partition tt permutation inputs permutation-reset semiautomaton Proof proved reduced automaton regular expression right congruence right cosets right-hand side rules of inference Section semi semiauto semigroup isomorphic set of words simple group subgroup H subsemiautomaton table of derivatives transition graph two-state reset semiautomata universal algebra vertex weak homomorphism