  We consider an asynchronous system with transitions corresponding to the
instructions of a computer system. For each instruction, a runtime is given. We
propose a mathematical model, allowing us to construct an algorithm for finding
the minimum time of the parallel process with a given trace. We consider a
problem of constructing a parallel process which transforms the initial state
to given and has the minimum execution time. We show that it is reduced to the
problem of finding the shortest path in a directed graph with edge lengths
equal to 1.
