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Публікація Use of parallelism in finite state machines. Mathematical level(EWDTW, 2004) Krivoulya, G. F.; Nemchenko, O.The method of the description of parallel systems using finite state machines is examined. The mathematical model proposed in this article can use both for the description and for synthesis of synchronous and asynchronous parallel systems with usage of abstractions of parallel programming: threads, processes, flags, mutexes, semaphores and complex synchronizations. One of methods of computing systems productivity rising is usage of parallelism in operation. Exists two ways of parallel data processing: strictly parallelism and command pipe [1]. The command pipe is present at personal computers, parallel processing is present, as a rule, in specialized computing systems - on parallel computers. Parallel computer architectures strongly differ one from each other. In There is a problem of code portability - the program fulfilled effectively on one system, practically does not use resources on another. In other words, there is weak program portability and the compiled code for parallel computers. Parallelism can be created on the basis of several computing units. Such system becomes complicated over availability of such units, commutative equipment and interconnection interfaces. It is much better to create the parallel arrangement in one chip with the required architecture. In this case the programmable logic CPLD, FPGA, can be used. In this article the mathematical model of a parallel finite state machine (FSM) digital automaton is discussed which can be used for the description of parallel algorithms and for its synthesis.