Calculating skeleton matrix of asynchronous sequential machines based on the semi‐tensor product of matrices

Abstract

In this study, the problem of calculating the skeleton matrix for asynchronous sequential machine (ASMs) is addressed in the framework of the semi-tensor product (STP) of matrices. By applying the STP of matrices and Boolean algebra, a new algebraic expression of ASMs is deduced. By utilising the algebraic expression, the skeleton matrix of ASMs can be easily derived, then the notion of generalised skeleton matrix is further defined for the ASMs with infinite cycles or critical races, and an algorithm of calculating the generalised skeleton matrix is also proposed. For the model matching problem of input/output ASMs, a novel approach is proposed to calculate reachability indictor and generalised fused skeleton matrix. Two examples are presented to illustrate the effectiveness of the proposed results.