Husainov

We study asynchronous systems used for mathematical modeling of the parallel computer system. It is considered as a set with partially trace monoid action. This allowed us to introduce homomorphisms of asynchronous systems as corresponding polygonal morphisms. Asynchronous systems with time function are studied using these homomorphisms. An algorithm for computing the minimal execution time of parallel processes in asynchronous systems is constructed. The conditions of homomorphisms of asynchronous systems minimal execution time keeping are found. The algorithm is used for compute of execution time of parallel processes, which consists of Petri net transitions. There are examples of computing minimal execution time for pseudo-pipeline and wave system. An experiment realized with multithreaded application that is built on a given Petri net is described. The experiment confirms the method of estimating the minimum execution time of the parallel process.