科研之友
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摘要
This paper presents some structural properties of a generalized Petri net (PN) with an algorithm to determine the (partial) conservativeness and (partial) consistency of the net. A product incidence matrix A = CCT or (A) over tilde = C-T C is defined and used to further improve the relations among PNs, linear inequalities and matrix analysis. Thus, based on Cramer's Rule, a new approach for the study of the solution of a linear system is given in terms of certain sub-determinants of the coefficient matrix and an efficient algorithm is proposed to compute these sub-determinants. The paper extends the common necessary and/or sufficient conditions for conservativeness and consistency in previous papers and some examples are designed to explain the conclusions finally.
