The saturation algorithm for symbolic state-space exploration

Ciardo, Gianfranco; Marmorstein, Robert; Siminiceanu, Radu

doi:10.1007/s10009-005-0188-7

Cited by 54 publications

(51 citation statements)

References 39 publications

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“…Saturation is a state space traversal strategy specifically tailored to work on decision diagram representations [4]. The problem of state space generation is the computation of the set of system states reachable from one or more initial states I.…”

Section: Saturationmentioning

confidence: 99%

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Getting the Priorities Right: Saturation for Prioritised Petri Nets

Marussy

Molnár

Vörös

et al. 2017

Application and Theory of Petri Nets and Concurrency

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Abstract. Prioritised Petri net is a powerful modelling language that often constitutes the core of even more expressive modelling languages such as GSPNs (Generalized Stochastic Petri nets). The saturation state space traversal algorithm has proved to be efficient for non-prioritised concurrent models. Previous works showed that priorities may be encoded into the transition relation, but doing so defeats the main idea of saturation by spoiling the locality of transitions. This paper presents an extension of saturation to natively handle priorities by considering the priority-related enabledness of transitions separately, adopting the idea of constrained saturation. To encode the highest priority of enabled transitions in every state we introduce edge-valued interval decision diagrams. We show that in case of Petri nets, this data structure can be constructed offline. According to preliminary measurements, the proposed solution scales better than previously known matrix decision diagrambased approaches, paving the way towards efficient stochastic analysis of GSPNs and the model checking of prioritised models.

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Section: Saturationmentioning

confidence: 99%

“…Saturation is one of the most efficient symbolic algorithms when it comes to concurrent, asynchronous systems [4]. It works on a decision diagram representation of the state space and its iteration strategy follows the structure of the diagram.…”

Section: Introductionmentioning

confidence: 99%

Getting the Priorities Right: Saturation for Prioritised Petri Nets

Marussy

Molnár

Vörös

et al. 2017

Application and Theory of Petri Nets and Concurrency

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“…In [8] we observed that a chaining [28] order where these subsets are applied to the MDD in bottom-up fashion results in good speedups with respect to a strict BFS symbolic state-space generation. The bounded version of chaining is shown in Fig.…”

Section: Introductionmentioning

confidence: 90%

“…3 does not even access nodes below Bot (α), only Union does. This has been shown to significantly reduce the peak number of MDD nodes [8].…”

Section: Bounded Reachability Checking Using Decision Diagramsmentioning

confidence: 99%

“…In several studies, Saturation has been shown superior to BFS-style iterations when symbolically computing least fixpoints for asynchronous models [8,9,10]. The challenge in adapting Saturation to bounded model checking lies in the need to bound the symbolic traversal in the nested fixpoint computations.…”

Section: Bounded Reachability Checking Using Decision Diagramsmentioning

confidence: 99%

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Bounded Reachability Checking of Asynchronous Systems Using Decision Diagrams

Ciardo

Lüttgen

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. Bounded reachability or model checking is widely believed to work poorly when using decision diagrams instead of SAT procedures. Recent research suggests this to be untrue with regards to synchronous systems, particularly digital circuits. This paper shows that the belief is also a myth for asynchronous systems, such as models specified by Petri nets. We propose Bounded Saturation, a new algorithm to compute bounded state spaces using Multi-way Decision Diagrams (MDDs). This is based on the established Saturation algorithm which benefits from a non-standard search strategy that is very different from breadth-first search. To bound Saturation, we employ Edge-Valued MDDs and rework its search strategy. Experimental results show that our algorithm often, but not always, compares favorably against two SAT-based approaches advocated in the literature for deadlock checking in Petri nets.

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Symbolic Model Checking for Avionics

Gnesi

Margaria

2012

Formal Methods for Industrial Critical Systems

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The saturation algorithm for symbolic state-space exploration

Cited by 54 publications

References 39 publications

Getting the Priorities Right: Saturation for Prioritised Petri Nets

Getting the Priorities Right: Saturation for Prioritised Petri Nets

Bounded Reachability Checking of Asynchronous Systems Using Decision Diagrams

Symbolic Model Checking for Avionics

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