On the complete simulation of DOL schemes and locally catenative schemes

Let (Σ, h) be a DOL scheme where h is a homomorphism from Σ^* to Σ^*. (Σ, h) is said to completely simulate another DOL scheme (Δ, g) if hf = fg and hⁿ = fr} for some injective homomorphism f, some positive integer n, and some homomorphism r. The main results of this paper are: (1) Each complete simulation can be decomposed into a series of “primitive” simulations. (2) It is decidable whether or not there exists a standard locally catenative scheme which is simulated by a given DOL scheme.