Symbolic analysis of bounded Petri nets (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.

Petri net analysis using boolean manipulation

1994

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.

DSSZ-MC – A Tool for Symbolic Analysis of Extended Petri Nets

Lecture Notes in Computer Science, 2009

DSSZ-MC supports the symbolic analysis of bounded place/ transition Petri nets extended by read, inhibitor, equal, and reset arcs. No previous knowledge of the precise boundedness degree is required. It contains tools for the efficient analysis of standard properties (boundedness, liveness, reversibility) and CTL model checking, built on an objectoriented implementation of Zero-suppressed Binary Decision Diagrams and Interval Decision Diagrams. The main features are saturation-based state space generation, analysis of strongly connected components, dead state analysis with trace generation, and CTL model checking by limited backward reachability analysis. The tool is available for Windows, Linux, and Mac/OS.

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.

A Symbolic State-Transition Graph for a Class of Dynamic Petri Nets

2009

The design of dynamic, adaptable discrete-event systems calls for adequate modeling formalisms and tools in order to manage possible changes occurring during system's lifecycle. A com- mon approach is to pollute the design with details not concerning the current system behavior, rather its evolution. That hampers analysis, reuse and main- tenance in general. A Petri net-based reective model (based on classical Petri nets) was recently proposed to support dynamic discrete-event system's design, and was applied to dynamic workow's management. Behind there is the idea that keeping functional as- pects separated from evolutionary ones, and applying evolution to the (current) system only when neces- sary, results in a clean formal model for dynamic sys- tems. This model preserves the ability of verifying properties typical of classical Petri nets. As a rst step toward the implementation (in the short time) of a discrete-event simulator, Reective Petri nets are provided in thi...

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 ...

Structural Methods Applied to the Symbolic Analysis of Petri Nets

International Workshop on Logic & Synthesis, 1998

Symbolic techniques based on Binary Decision Diagrams have emerged as one of the possible strategies to overcome the state exposition problem in the analysis of systems modeled as Petri nets. The results on structural theory of Petri nets obtained in the last few decad es can be used to improve the symbolic analysis and to alleviate the state exposition problem.

Linear time analysis of properties of conflict-free and general Petri nets

Theoretical Computer Science, 2011

We introduce the notion of T -path within Petri nets, and propose a simple approach, based on previous work developed for directed hypergraphs, in order to determine structural properties of nets; in particular, we study the relationships between T -paths in a Petri net and firable sequences of transitions.

The Possibilities of Modeling Petri Nets and Their Extensions

Computer Simulation [Working Title], 2019

This chapter is dedicated to several structure features of Petri nets. There is detailed description of appropriate access in Petri nets and reachable tree mechanism construction. There is an algorithm that describes the minimum sequence of possible transitions. The algorithm developed by us finds the shortest possible sequence for the network promotion state, which transfers the mentioned network state to the coverage state. The corresponding theorem is proven, which states that due to the describing algorithm, the number of transitions in the covering state is minimal. This chapter studies the interrelation of languages of colored Petri nets and traditional formal languages. The Venn diagram, modified by the author, is presented, which shows the relationship between the languages of the colored Petri nets and some traditional languages. As a result, it is shown that the language class of colored Petri nets includes an entire class of context-free languages and some other classes. The results obtained show that it is not possible to model the Patil problem using the well-known semaphores P and V or classical Petri nets, so the mentioned systems have limited properties.

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.