Simulation, reduction and preservation of correctness properties of parallel systems

A unified formal treatment of simulation and reduction concepts for parallel computation systems is given. A computation homomorphism, a notion introduced by Kasai and Miller (1979), is used to study the correctness properties of parallel computation systems. The concept of reduction induced by a surjective computation of homomorphism is introduced and its relationship with the similar concept of simulation is studied. The use of reduction is combined to verification techniques based on temporal logic. The results of Berthelot et al. (1979), Kasai and Miller (1979) and Kwong (1977) are unified and generalized.