Efficient simplicity testing of automata

Abstract

Let V be a pseudovariety of finite semigroups; an automation A = (X, Σ, M) is called V -type if the transformation semigroup of A belongs to V . Polynomial-time algorithms for testing whether an automaton A = (X, Σ, M) is S -type, RS -type, LS -type or RS ⋁ LS -type are given, where S, RS and LS denotes, respectively, the pseudovarieties of all finite simple semigropus, all finite right simple semigroups are all finite left simple semigroups.