Finite state machines, being a mathematical abstraction, allow you to perceive information from the control object, process it and give signals to control the object. The disadvantages of the representation of complex production systems by a set of finite state machines include the complexity of carrying out logical and set-theoretic operations on them and the complexity of describing the parallelism that occurs in the operation of complex production systems. When specifying a finite state machine in the matrix–predicate form, due to the information redundancy, it is possible to avoid these difficulties. Matrix–predicate method allows you to uniquely set the finite state machine square matrix, which makes it possible to use the methods of the theory of matrices during the set–theoretic operations on them and it is possible to avoid isomorphism. The paper presents the developed methods of representation of a finite state machine using a multi-place predicate, which greatly simplifies its task.

Keywords: finite state machine, graph, matrix, predicate, algorithm, matrix–predicate method, graph incident, tuple, Cartesian product, complex production systems