A definition of Petri net symmetries is given and an algorithm is introduced, which computes these symmetries. Then three examples are given how algorithms from different fields of Petri net analysis can be improved using symmetries, namely computation of reachability graphs, semipositive place invariants and structural deadlocks,

Validation of industrial designs is becoming more challenging as technology advances and demand for higher performance increases. One of the most suitable debugging aids is automatic formal verification. Unlike simulation, which tests behaviors under a specific execution, automatic formal verification tests behaviors under all possible executions of a system. Therefore, it is able to detect errors that cannot be reliably repeated using simulation. However, automatic formal verification is limited by the state explosion problem. The number of states for practical systems is often too large to check exhaustively within the limited time and memory that is available. Existing solutions have widened the range of verifiable systems, but they are either insufficient or hard to use. This thesis presents several techniques for reducing the number of states that are examined in automatic formal verification. These techniques have been evaluated on high-level descriptions of industrial designs, ...

The goal of net reduction is to increase the effectiveness of Petrinet -based real-time program analysis. Petri-net-based analysis, like all reachability-based methods, suffers from the state explosion problem. Petri net reduction is one key method for combating this problem. In this paper, we extend several rules for the reduction of ordinary Petri nets to work with time Petri nets. We introduce a notion of equivalence among time Petri nets, and prove that our reduction rules yield equivalent nets. This notion of equivalence guarantees that crucial timing and concurrency properties are preserved. Partially supported by NSF grants CCR-9108753 and CCR-9314258. Email: sloan@eecs.uic.edu. y Partially supported by NSF grants CCR-9109231 and CCR-9314258. Email: buy@eecs.uic.edu. 1 Introduction Petri nets have proven to be a very useful tool for the analysis of concurrent systems. To date several approaches have been defined that use Petri nets to model a system being analyzed (e.g...

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We present a fully automatic framework for identifying symmetries in structural descriptions of digital circuits and CTL* formulas and using them in a model checker. We show how the set of sub-formulas of a formula can be partitioned into equivalence classes so that truth values for only one sub-formula in any class need be evaluated for model checking. We unify and extend the theories developed by Clarke et al [CEFJ96] and Emerson and Sistla [ES96] for symmetries in Kripke structures. We formalize the notion of structural symmetries in net-list descriptions of digital circuits and CTL* formulas. We show how they relate to symmetries in the corresponding Kripke structures. We also show how such symmetries can automatically be extracted by constructing a suitable directed labeled graph and computing its automorphism group. We present a novel fast algorithm for solving the graph automorphism problem for directed labeled graphs.

. We present three methods for the integration of symmetries into reachability analysis. Two of them lead to perfect reduction but their runtime depends on the symmetry structure. The third one works always fast but does not always yield perfect reduction. Keywords: (Theory) Computer tools for nets 1 Introduction Symmetric structure yields symmetric behavior. Thus, symmetries can be employed to reduce the size of reachability graphs. Instead of storing all states, only (representatives of) equivalence classes of states are stored. There are two major problems that need to be solved in the context of symmetries. Before starting reachability graph generation, we need to investigate the symmetries of the system. During graph generation, we need to decide repeatedly whether for a (recently generated) state an equivalent one has been explored earlier. In the context of high level Petri nets, we can use operations and relations of the color sets to describe the symmetries symbolically...

The symmetry reduction method is a technique for alleviating the combinatorial explosion problem arising in the state space analysis of concurrent systems. This thesis studies various issues involved in the method. The focus is on systems modeled with Petri nets and similar formalisms, such as the Murϕ description language. For place/transition nets, the computational complexity of the sub-tasks involved in the method is established. The problems of finding the symmetries of a net, comparing whether two markings are equivalent under the symmetries, producing canonical representatives for markings, and deciding whether a marking symmetrically covers another are classified to well-known complexity classes. New algorithms for the central task of producing canonical representatives for markings are presented. The algorithms apply and combine techniques from computational group theory and from the algorithms

We propose to extend existing Petri-net-based tools for concurrency analysis to real-time analysis. The goal is to create a fully automated system, which starts from code in a higher level language for real-time programming, and answers programmers' queries about timing properties of the code. The key difficulty with all reachability-based approaches is that the state space quickly becomes intractably large. To circumvent this state explosion problem, we propose using a combination of several heuristics for model reduction and state space reduction that have been effective for untimed concurrency analysis. In: Proceedings of the Seventh International Workshop on Software Specification and Design, pp. 56--60, December 1993, IEEE Computer Society Press. 1 Introduction The analysis of real-time software is very difficult. Indeed, the activities of design, implementation and testing are costly and complex even for traditional software, considerably more costly and complex for untimed co...

We present a first report on our PARTS toolset for the automated static analysis of real-time systems. The PARTS toolset is based upon a timed extension of Petri nets. Our simple time Petri nets or STP nets are specifically aimed at facilitating real-time analysis. Our analysis approach uses the state space of an STP net in order to answer queries about the concurrency and timing behavior of the corresponding system. An attractive feature of STP nets is that they support a variety of techniques for controlling the number of states that must be explicitly enumerated. These techniques were originally defined for the analysis of concurrency properties of untimed systems, and in this paper we discuss the extension of each to the timed domain. We also report on some preliminary experimental results that we obtained by running our toolset on examples of real-time systems. In: Proceedings of the 1994 Internatinal Symposium on Software Testing and Analysis (ISSTA '94), pp. 228--239, August 1...

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