Liveness in bounded Petri nets which are covered by T-invariants

Structure Theory of Petri Nets

“…Since the publication of this meritorious piece of work, further structural results in a similar vein have been discovered, e.g. : [Esp98] (NP-completeness of reachability in live and safe FC-systems); the blocking theorem described in section 3.6 [GHM03,Weh10]; general reachability criteria as described in section 3.7, which are due to Hideki Yamasaki, Jeng S. Huang and Tadao Murata [YHM01], with related results in [LR94,MM98,YY03]; and the proof, by Joachim Wehler [Weh09], of an old conjecture on a subclass of free-choice systems by Hartmann Genrich and P.S. Thiagarajan [GT84], making a connection to the almost equally old notion of frozen tokens [BM85]; not to mention many generalisations and extensions of these results, e.g.…”

Supervisory Control of Discrete Event Systems Using Petri Nets

“…This section includes a procedure developed by [Lautenbach and Ridder, 1994] for using transition invariants to determine the liveness of a class of nets. Several researchers have studied deadlock avoidance in their work on the modeling and control of manufacturing systems; these include [Ezpeleta et al, 1995, Bogdan and Lewis, 1997, Xing et al, 1996.…”

“…Another sufficient test for liveness is presented below. [Lautenbach and Ridder, 1994] present an algorithm for determining if a net is live, given that it contains a covering nonnegative transition invariant (T-invariant). The first two steps of the algorithm involve transformations of the ofthe PN graph such that the transformed net contains a minimal covering canonical T-invariant 1 while maintaining the same reachable state space as the original net.…”

“…[Valette et al, 1985, Valette, 1986 have explored the use of Petri nets as analytical and computational models for the representation of discrete event system controllers and have used Petri net place invariants as an analysis tool. [Lautenbach and Ridder, 1994] use transition invariants as a means of examining and enforcing "liveness" on a Petri net. [Barkaoui and Abdallah, 1995 all make use of place invariants as a tool in the prevention of "deadlock" (see chapter 6).…”

Extended Synchronized Choice Nets

“…Based on simple structures, we derived the simple conditions plus an integrated algorithm with polynomial time complexity for verification of SNC, liveness, reachability and reversibility. Barkaoui et al [3] and Lautenbach and Ridder [6], however, cannot provide integrated algorithms for their new classes of nets to verify a given net is in the new classes and also live. Their algorithms only work for bounded nets in the new classes.…”