Automata, Languages, and Machines

2-class aperiodic assume boolean closure Chapter Clearly closed S-variety complete congruence Consequently consider containing Corollary denote equations EXAMPLE EXERCISE exists following conditions follows from Proposition function f given group G Holonomy idempotent implies Imre Simon inclusion injective integer isomorphic Krohn–Rhodes left action Let f Let G minimal automaton nilpotent non-empty obtain order ideal p-group partial function PF(Q pºp prime PROPOSITION 2.1 prove q e Q quotient recognizable subset Rees matrix semigroup relational covering RSgp Sa e satisfies semidirect product sequential functions sequential machine sequential partial function Show singleton submonoid subsemigroup suffices surjective functional surjective morphism syntactic invariants syntactic monoid Theorem 2.1 tºp Transformation Semigroups ts's U.-free unit element unitary monoid variety weakly closed class wreath product