Linear Algebraic Techniques for Place/Transition Nets

Mathematical programming approach to the Petri nets reachability problem

“…• Last ones are based on the PN State Equation (cf. Proposition 1): we can distinguish parameterized analysis [22] and algebraic methods [20].…”

Automatic code generation from high-level Petri-Nets for model driven systems engineering

“…Generally, cyclic structures in a Petri-Net may be identified by means of invariant analysis (Lautenbach, 1987). Since this analysis technique is based on low-level Place/Transition-Nets, a high-level model needs to be preprocessed prior to invariant analysis with the following steps:…”

Supervisory Control of Discrete Event Systems Using Petri Nets

“…properties that depend only on the topological structure of the Petri net and not on the net's initial marking, are the net invariants. Invariants are important means for analyzing Petri nets since they allow for the net's structure to be investigated independently of any dynamic process [Lautenbach, 1987].…”

“…The two places form both a trap and a siphon, however this net contains no invariants. Algorithms for computing the traps or siphons of a Petri net appear in [Ezpeleta et al, 1993] and [Lautenbach, 1987]. The work of [Ezpeleta et al, 1993] includes a comparison of several siphon-calculation techniques as well as their own algorithm, which is presented below.…”