Petri net analysis using boolean manipulation (original) (raw)

Symbolic Petri Net Analysis Using Boolean Manipulation

1998

This paper presents a novel analysis approach for bounded Petri nets. The net behavior is modeled by boolean functions, thus reducing reasoning about Petri nets to boolean calculation. The state explosion problem is managed by using Binary Decision Diagrams (BDDs), which are capable to represent large sets of markings in small data structures. The ability of Petri nets to model systems, the exibility and generality of boolean algebras, and the e cient implementation of BDDs, provide a general environment to handle a large variety of problems. Examples are presented that show how all the reachable states (10 18) of a Petri net can be e ciently calculated and represented with a small BDD (10 3 nodes). Properties requiring an exhaustive analysis of the state space can be veri ed in polynomial time in the size of the BDD.

Symbolic analysis of bounded Petri nets

IEEE Transactions on Computers, 2001

AbstractÐThis work presents a symbolic approach for the analysis of bounded Petri nets. The structure and behavior of the Petri net is symbolically modeled by using Boolean functions, thus reducing reasoning about Petri nets to Boolean calculation. The set of reachable markings is calculated by symbolically firing the transitions in the Petri net. Highly concurrent systems suffer from the state explosion problem produced by an exponential increase of the number of reachable states. This state explosion is handled by using Binary Decision Diagrams (BDDs) which are capable of representing large sets of markings with small data structures. Petri nets have the ability to model a large variety of systems and the flexibility to describe causality, concurrency, and conditional relations. The manipulation of vast state spaces generated by Petri nets enables the efficient analysis of a wide range of problems, e.g., deadlock freeness, liveness, and concurrency. A number of examples are presented in order to show how large reachability sets can be generated, represented, and analyzed with moderate BDD sizes. By using this symbolic framework, properties requiring an exhaustive analysis of the reachability graph can be efficiently verified.

A Petri Net Modeling Approach Based on Boolean Function Transition

2012 International Symposium on Computer, Consumer and Control, 2012

A Petri Net is a mathematical modeling language for the description of distributed systems. A Petri net is a directed bipartite graph, in which the elements consist of place, transition, and arc. A Petri Net offers a kind of graphical notation for stepwise processes which include choice, iteration, and concurrent execution. However, when the system is getting large, the complexity of Petri Nets will be increased more quickly. In this paper, we propose a new Petri Net modeling language which is based on the Boolean Function Transition (BFT-PN, for short). Via combining the function with Boolean mathematic, it can describe both of PTP (Place-Transition-Place) table and the state transition of system more easily. BFT-PN can also reduce the complexity of transition of system on when the system is getting large and having a lot of events. In the other words, it can be dealt with very complex transition states by stepwise process not only more easily but also very clearly.

Efficient encoding schemes for symbolic analysis of Petri nets

Proceedings Design, Automation and Test in Europe, 1998

Petri nets are a graph-based formalism appropriate to model concurrent systems such as asynchronous circuits or network protocols. Symbolic techniques based on Binary Decision Diagrams (BDDs) have emerged as one of the strategies to overcome the state explosion problem in the analysis of systems modeled by Petri nets. The existing techniques for state encoding use a variableper-place strategy that leads to encoding schemes with very low density. This drawback has been partially mitigated by using Zero-Suppressed BDDs, that provide a typical reduction of BDD sizes by a factor of two. This work presents novel encoding schemes for Petri nets. By using algebraic techniques to analyze the topology of the net, sets of places "structurally related" can be derived and encoded by only using a logarithmic number of boolean variables. Such approach allows to drastically decrease the number of variables for state encoding and reduce memory and CPU requirements significantly.

A Symbolic Algorithm for the Synthesis of Bounded Petri Nets

2008

This paper presents an algorithm for the synthesis of bounded Petri nets from transition systems. A bounded Petri net is always provided in case it exists. Otherwise, the events are split into several transitions to guarantee the synthesis of a Petri net with bisimilar behavior. The algorithm uses symbolic representations of multisets of states to efficiently generate all the minimal regions. The algorithm has been implemented in a tool. Experimental results show a significant net reduction when compared with approaches for the synthesis of safe Petri nets.

Construction of a Crisp Boolean Petri Net from a 1-safe Petri Net

International Journal of Computer Applications, 2013

The concept of a Petri net, a tool for the study of certain discrete dynamical systems, was invented in 1939 by Carl Adam Petri. In the attempt to characterize Boolean Petri nets, we discovered a subclass of Boolean Petri net called the crisp Boolean Petri net, viz., the one that generates every binary vector as its marking vectors exactly once. In this paper, the construction of a crisp Boolean Petri net from a 1-safe Petri net has been shown.

Structural Methods to Improve the Symbolic Analysis of Petri Nets

Application and Theory of Petri Nets …, 1999

Abstract. Symbolic techniques based on BDDs (Binary Decision Di-agrams) have emerged as an efficient strategy for the analysis of Petri nets. The existing techniques for the symbolic encoding of each marking use a fixed set of variables per place, leading to encoding schemes with ...

A boolean model for enumerating minimal siphons and traps in petri nets

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2012

Petri nets are a simple formalism for modeling concurrent computation. Recently, they have emerged as a promising tool for modeling and analyzing biochemical interaction networks, bridging the gap between purely qualitative and quantitative models. Biological networks can indeed be large and complex, which makes their study difficult and computationally challenging. In this paper, we focus on two structural properties of Petri nets, siphons and traps, that bring us information about the persistence of some molecular species. We present two methods for enumerating all minimal siphons and traps of a Petri net by iterating the resolution of Boolean satisfiability problems executed with either a SAT solver or a CLP(B) program. We compare the performances of these methods with respect to a state-of-the-art algorithm from the Petri net community. On a benchmark with 80 Petri nets from the Petriweb database and 403 Petri nets from curated biological models of the Biomodels database, we show that miniSAT and CLP(B) solvers are overall both faster by two orders of magnitude with respect to the dedicated algorithm. Furthermore, we analyse why these programs perform so well on even very large biological models and show the existence of hard instances in Petri nets with unbounded degrees.

Embedding an Arbitrary 1-safe Petri Net into a Boolean Petri Net

International Journal of Computer Applications, 2013

Petri nets are powerful mathematical formalism for designing and studying behaviors of a wide range of discrete dynamical event driven systems. The aim of this paper is to show that an arbitrary 1safe Petri net can be embedded as an induced subnet of a Boolean Petri net, viz., the one that generates every binary n-vector as its marking vector.