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Set-theoretic Model of Digital Systems Functioning

Ivannikov A., Romanov A., Stempkovsky A.

For projects of digital systems, defined by the circuit diagram of blocks connection and software, it is proposed to use a mathematical model in the terms of the set theory and the theory of stationary dynamic systems. Due to the fact that the supply of input signals to the digital system in some cases depends on the output ready signals, the concept of input and output interactions is introduced. These interactions are sequences of events each of which is the change of the input and output variables from one value to another at a particular time. The aim of a digital system project debugging is formulated in terms of a comparison of the family of stationary dynamic systems describing the desired external behavior of a digital system and a family of systems defined by the structure of the digital system design.