Structural Methods to Improve the Symbolic Analysis of Petri Nets (original) (raw)

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.

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.

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.

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 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...

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.

Comparison of encoding schemes for symbolic model checking of bounded petri nets

I would like to dedicate this thesis to my parents who have been a source of inspiration and encouragement to me all throughout my life. A very special thanks to Prof. Andrew Miner for his constant support and guidance. I learnt a lot from him and would like to thank him from all my heart. I would also like to take this opportunity to thank Junaid Babar and my committee members, Prof. Samik Basu and Prof. Robyn Lutz for their help and support. Thanks to my siblings for their unconditional love that has helped me succeed at every step. Finally, I would like to thank my friend Shantanu, who instilled in me the confidence that I am capable of doing anything I put my mind to.