Reachability Analysis Of Petri Nets Research Articles

Stubborn versus structural reductions for Petri nets

Partial order and structural reduction techniques are some of the most beneficial methods for state space reduction in reachability analysis of Petri nets. This is among others documented by the fact that these techniques are used by the leading tools in the annual Model Checking Contest (MCC) of Petri net tools. We suggest improved versions of a partial order reduction based on stubborn sets and of a structural reduction with additional new reduction rules, and we extend both methods for the application on Petri nets with weighted arcs and weighted inhibitor arcs. All algorithms are implemented in the open-source verification tool TAPAAL and evaluated on a large benchmark of Petri net models from MCC'17, including a comparison with the tool LoLA (the last year winner of the competition). The experiments document that both methods provide significant state space reductions and, even more importantly, that their combination is indeed beneficial as a further nontrivial state space reduction can be achieved.

Optimisation of block erection scheduling based on a Petri net and discrete PSO

The shipyard block erection system (SBES) is a typical discrete-event dynamic system. To model multiprocessing paths and a concurrent assembly procedure, a timed Petri net (TPN) is proposed. The definition of a Petri net is extended to accord with the real-world SBES organisation. The basic TPN modules are presented to model the corresponding variable structures in the SBES, and then the scheduling model of the whole SBES is easily constructed. A modified discrete particle swarm optimisation (PSO) based on the reachability analysis of Petri nets is developed for scheduling of the SBES. In the proposed algorithm, particles are coded by welding transitions and selecting places of the TPN model, and then the collaboration and competition of particle individuals is simulated by crossover and mutation operators in a genetic algorithm. Numerical simulation suggests that the proposed TPN–PSO scheduler can provide an improvement over the conventional scheduling method. Finally, a case study of the optimisation of a back block erection process is provided to illustrate the effectiveness of the method.

A Petri net approach for simple assembly line balancing problems

A simple assembly line balancing problem of type-1 (SALBP-1) aims to minimize the number of workstations for a given cycle time. In the relevant literature, several heuristics based on a branch-and-bound procedure, tabu search, and genetic algorithms (GAs) were proposed to solve SALBP-1. In this paper, an algorithm based on the reachability analysis of Petri nets is developed for SALBP-1. The proposed algorithm searches enabled transitions (or assignable tasks) in the Petri net model of precedence relations between tasks, and then the task minimizing the idle time is assigned to the station under consideration. The algorithm is coded in MATLAB, and its efficiency is tested on Talbot’s and Hoffmann’s benchmark datasets according to some performance measures and classifications. A computational study validates its effectiveness on Tonge’s 70-task problem by comparison with optimal solutions of traditional heuristics and a GA.

Optimal Legal Firing Sequence of Petri Nets Using Linear Programming

Petri nets (PNs) are a reliable graphical and mathematical modeling tool for the formal modeling and validation of systems (W. Reisig, A Primer in Petri Net Design, Springer-Verlag: Berlin, Heidelberg, 1992). Applications of PNs include discrete event dynamic systems (DEDS) that are recognized as being concurrent, asynchronous, distributed, parallel, and/or nondeterministic. It is also a powerful formal method for the analysis of concurrent, embedded, and distributed finite state systems (K. Varpaaniemi, Series A: Research Reports, No. 26, Helsinki University of Technology, Digital Systems Laboratory, Oct. 1993). The reachability analysis of PNs is strategically significant as it captures the dynamic behavior of the system as well as providing efficient verification of the correctness of the model. Few linear programming (LP)-based methods can be found that address the reachability problem, and some of these are suitable for optimal control problems. However, due to an inherent state explosion they are difficult to implement; other methods run easily into deadlock as they lack appropriate mechanisms to avoid the firing of critical transitions (T. Matsumoto and A. Tarek, in Proceedings of the 35th IEEE Conference on Decision and Control, Kobe, Japan, 1996-12, pp. 4459–4468). In this paper an improved and easy to implement method is proposed that combines the Optimality Principle and Linear Programming (OP + LP) techniques to find an Optimal Legal Firing Sequence (OLFS) in PNs. This method can be applied to ordinary PNs with self-loops, avoids deadlocks, and can also be used for general PNs having cycles.

Graph models for reachability analysis of concurrent programs

The problem of analyzing concurrent systems has been investigated by many researchers, and several solutions have been proposed. Among the proposed techniques, reachability analysis—systematic enumeration of reachable states in a finite-state model—is attractive because it is conceptually simple and relatively straightforward to automate and can be used in conjunction with model-checking procedures to check for application-specific as well as general properties. This article shows that the nature of the translation from source code to a modeling formalism is of greater practical importance than the underlying formalism. Features identified as pragmatically important are the representation of internal choice, selection of a dynamic or static matching rule, and the ease of applying reductions. Since combinatorial explosion is the primary impediment to application of reachability analysis, a particular concern in choosing a model is facilitating divide-and-conquer analysis of large programs. Recently, much interest in finite-state verification systems has centered on algebraic theories of concurrency. Algebraic structure can be used to decompose reachability analysis based on a flowgraph model. The semantic equivalence of graph and Petri net-based models suggests that one ought to be able to apply a similar strategy for decomposing Petri nets. We describe how category-theoretic treatments of Petri nets provide a basis for decomposition of Petri net reachability analysis.

Local area network implementation of petri net reachability analysis

The parallelization of systems can result in faster and more efficient operation. Local Area Networks (LANs) are gaining importance for implementing parallel computers because of the availability and experience on the IBM PC. According to the Wall Street Journal May 23, 1990 in the article ‘PC networks begin to oust mainframes in some companies’, the IBM PS/2 LAN is touted as working as a “very small mainframe”, and their inexpensive yet reliable software is noted. One possible LAN utilization is as a parallel computer system for certain problems. The Petri Net is a graph model with the ability to depict concurrency and parallelism, the ability to describe a system at various levels of abstraction, and can show control elements using tokens. In this paper, we utilize the LAN to compute the parallel portions of the Petri net reachability tree.