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Elementary Definitions and Examples
Algebraic Machine Theory and Logical Design
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0-minimal ideal 0-simple semigroup algebraic theory automata automaton block cascade Chapter combinatorial semigroup commutative compact semigroup complexity component congruence set contained context-free context-free languages coordinate map 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 integer inverse irreducible isomorphism kernel Krohn Krohn-Rhodes left ideal left simple Lemma Let s1 mapping semigroup Math maximal subgroup morphism multiplication noncombinatorial nontrivial nonzero normal subgroup notation null null semigroup output permutation phism prime decomposition theorem PROOF Proposition prove reader Rees matrix semigroup respectively restricted Rhodes satisfies Schutzenberger Sect semidirect product series-parallel stimulus subsemigroup subset Suppose syntactic monoid topological transformation transformation semigroup transition union of groups unique verify wreath product zero