Structural Methods to Improve the Symbolic Analysis of Petri Nets

Abstract

Abstract. Symbolic techniques based on BDDs (Binary Decision Diagrams) have emerged as an e cient strategy for the analysis of Petri nets. The existing techniques for the symbolic encoding of each marking u s e a x e d s e t o f v ariables per place, leading to encoding schemes with very low density. This drawback has been previously mitigated by u s i n g Zero-Suppressed BDDs, that provide a typical reduction of BDD sizes by a factor of two. Structural Petri net theory provides P-invariants that help to derive more e cient encoding schemes for the BDD representations of markings. P-invariants also provide a mechanism to identify conservative upper bounds for the reachable markings. The unreachable markings determined by the upper bound can be used to alleviate both the calculation of the exact reachability set and the scrutiny of properties. Such approach allows to drastically decrease the numberofvariables for marking encoding and reduce memory and CPU requirements signi cantly.

Symbolic analysis of bounded Petri nets

“…As mentioned in Section 6, the encoding methods for k-bounded nets must be further explored. The combination of symbolic methods with structural and linear programming techniques as described in [11], more powerful reduction methodologies, improved chaining traversal, and more compact BDD variable encoding are clear areas for future development. …”

“…Since their introduction by C.A. Petri in 1962 [11], Petri nets (PNs) have been extensively used in a wide range of areas such as communication protocols and networks, computer architecture, distributed systems, manufacturing planning, digital circuit synthesis and verification, and high-level synthesis.…”

Petri nets for modelling metabolic pathways: a survey

“…Just to mention a few, reduction rules may be used to simplify a net while preserving its interesting properties (see, e.g., [90]). Binary decision diagrams, or generalisations of them, can be fruitfully combined with static analysis (e.g, [93]) to simplify the reachability analysis. Abstract interpretation may be used to reduce the size of the net (see, e.g., [49]) and partial order semantics to check reachability, coverability and absence of deadlocks and to model check behavioural logics for PNs [46].…”

Interval diagrams for efficient symbolic verification of process networks

“…In [37], zero-suppressed BDDs are used instead of regular BDDs to speed up the computation. General deficiencies of BDDs have been partially mitigated by applying novel encoding schemes to represent place contents [38], [39]. This is achieved by partially or completely transforming the Petri net into a set of finite state automata.…”