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Elementary Definitions and Examples
Algebraic Machine Theory and Logical Design
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0-minimal ideal 0-simple algebraic theory automata automaton block cascade Chapter combinatorial semigroup commutative compact semigroup complexity component congruence set contained context-free coordinate map cyclic group cyclic semigroup decomposition defined Definition denote direct product element epimorphism equivalence relation example Fact finite semigroups function given GM semigroup grammar group machine Hence homomor idempotent identity IG(S implies induction input integer inverse irreducible isomorphism Jt\G kernel Krohn Krohn-Rhodes left ideal left simple Lemma mapping semigroup Math maximal subgroup morphism multiplication noncombinatorial nontrivial nonzero notation null null semigroup output permutation phism prime decomposition theorem PROOF Proposition prove reader Rees matrix semigroup respectively restricted Rhodes satisfies semidirect product sequence series-parallel simple semigroup stimulus subsemigroup subset Suppose syntactic monoid transformation transformation semigroup transition union of groups unique verify W(Sf wreath product zero