Knitting technique and structural matrix for deadlock analysis and synthesis of Petri nets with sequential exclusion

Zhou and DiCesare (1991) presented the deadlock-free condition (DFC) of a Petri net (PN) containing sequential mutual exclusion (SME). This paper generalizes the DFC found by Zhou and DiCesare. The structural matrix (S-Matrix) plays an important role in the knitting technique because it is used to record the structural relationship among the processes and thus can be used to detect the violation of the synthetic rules upon a new generation of paths in the PN. To synthesize the SME, the construction of S-Matrix need to be enhanced. This paper also discusses the algorithm to construct the S-Matrix for the use of knitting technique to synthesize PNs with and without SME. An example of this algorithm is given