Modelling sequential circuits with cellular automata

Abstract

Cellular automata are powerful computational models for the study of physical systems. In the recent past they have been used to solve VLSI and CAD problems such as synthesis and testing of integrated circuits. In this paper it is shown how cellular automata may be used to model the behaviour of sequential circuits. The nice property of the proposed approach is that it provides an homogeneous representation of all the components of the circuit under investigation : primary inputs, flip-flops, primary outputs and their related cones of combinational logic are modelled in the same way by means of cellular automaton cells. Clearly, it is necessary to differentiate cells representing the flip-flops, from cells modelling the primary outputs and the primary inputs ; in fact, for cells of the first type the evolution rules are fixed, and they are simply given by the boolean functions realized by the cones of logic feeding the flip-flops. A similar argument applies to cells of the second type, with the difference that the states of these cells do not influence the next state of any other cell of the automaton. For cells of the third type, on the other hand, the next state functions are boolean functions whose characteristics depend on the aspect of the external world the user would like to model. The choice of such functions is not trivial, and to be effective requires an accurate study of both the functional meaning of each primary input in the context of the circuit to be modelled, and the relationship, if any, between the primary input lines. This paper includes a discussion, supported by experimental data, on the criteria to be used for the choice of these functions.