Improving Static Variable Orders Via Invariants

Ciardo, Gianfranco; Lüttgen, Gerald; Yu, Andy Jinqing

doi:10.1007/978-3-540-73094-1_8

Cited by 10 publications

(8 citation statements)

References 30 publications

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“…In a MPS, a weighted sum of tokens is constant in any marking. Therefore, we expect that a variable ordering that groups together MDD variables corresponding to places in the same NU/MPS should reduce the MDD size, due to the inter-dependence between the variables [11,25].…”

Section: Function Sloanmentioning

confidence: 99%

“…We assume that MDD levels encode Petri net places, i.e. we do not consider merging multiple places into a single level like in [11]. The state space generation algorithms employs saturation [10].…”

Section: Introductionmentioning

confidence: 99%

“…Note that Gradient-Π assumes that in the MDD we assign one place per level. Other techniques have instead used P-semiflows for identifying places to be grouped in a single level [11] or for state compression for binary decision diagrams [25]. These technique can be seen as orthogonal to the proposed one.…”

Section: Introductionmentioning

confidence: 99%

“…Indeed if x is a P-semiflow and m any state reachable from the initial state m 0 , we can write that x · m = K, where K is a constant value that can be computed from the initial state, K = x · m 0 . This suggests that all the places that are in the same P-semiflow (that is to say the set π x of all places p with a non-null value of x(p)) have a form of "circular" dependency and it is advisable to put them close together in the decision diagram [11]. The intuition is that each P-semiflow usually represents a local sub-component of a more complex model.…”

Section: Introductionmentioning

confidence: 99%

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Gradient-Based Variable Ordering of Decision Diagrams for Systems with Structural Units

Amparore

Beccuti

Donatelli

2017

Automated Technology for Verification and Analysis

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This paper presents Gradient-Π, a novel heuristics for finding the variable ordering of Decision Diagrams encoding the state space of Petri net systems. Gradient-Π combines the structural informations of the Petri net (either the set of minimal P-semiflows or, when available, the structure of the net in terms of "Nested Units") with a gradient-based greedy strategy inspired by methods for matrix bandwidth reduction. The value of the proposed heuristics is assessed on a public benchmark of Petri net models, showing that Gradient-Π can successfully exploit the structural information to produce good variable orderings.

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Section: Function Sloanmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Gradient-Based Variable Ordering of Decision Diagrams for Systems with Structural Units

Amparore

Beccuti

Donatelli

2017

Automated Technology for Verification and Analysis

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“…Furthermore, the efficiency of saturation is also highly dependent on the order of components. There are different heuristics to find a "proper" ordering, such as those introduced in [CLY07,SC06,TMIP04]. The algorithms presented in this paper assume that an ordering is already given.…”

Section: Symbolic Encodingmentioning

confidence: 99%

Component-wise incremental LTL model checking

et al. 2016

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Abstract. Efficient symbolic and explicit-state model checking approaches have been developed for the verification of linear time temporal logic (LTL) properties. Several attempts have been made to combine the advantages of the various algorithms. Model checking LTL properties usually poses two challenges: one must compute the synchronous product of the state space and the automaton model of the desired property, then look for counterexamples that is reduced to finding strongly connected components (SCCs) in the state space of the product. In case of concurrent systems, where the phenomenon of state space explosion often prevents the successful verification, the so-called saturation algorithm has proved its efficiency in state space exploration. This paper proposes a new approach that leverages the saturation algorithm both as an iteration strategy constructing the product directly, as well as in a new fixed-point computation algorithm to find strongly connected components on-the-fly by incrementally processing the components of the model. Complementing the search for SCCs, explicit techniques and component-wise abstractions are used to prove the absence of counterexamples. The resulting on-the-fly, incremental LTL model checking algorithm proved to scale well with the size of models, as the evaluation on models of the Model Checking Contest suggests.

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i $$_\mathrm {Rank}$$ : A Variable Order Metric for DEDS Subject to Linear Invariants

Amparore

Ciardo

Donatelli

et al. 2019

Tools and Algorithms for the Construction and Analysis of Systems

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Finding good variable orders for decision diagrams is essential for their effective use. We consider Multiway Decision Diagrams (MDDs) encoding a set of fixed-size vectors satisfying a set of linear invariants. Two critical applications of this problem are encoding the state space of a discrete-event discrete state system (DEDS) and encoding all solutions to a set of integer constraints. After studying the relations between the MDD structure and the constraints imposed by the linear invariants, we define i Rank , a new variable order metric that exploits the knowledge embedded in these invariants. We evaluate i Rank against other previously proposed metrics on a benchmark of 40 different DEDS and show that it is a better predictor of the MDD size and it is better at driving heuristics for the generation of good variable orders.

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Improving Static Variable Orders Via Invariants

Cited by 10 publications

References 30 publications

Gradient-Based Variable Ordering of Decision Diagrams for Systems with Structural Units

Gradient-Based Variable Ordering of Decision Diagrams for Systems with Structural Units

Component-wise incremental LTL model checking

i $$_\mathrm {Rank}$$ : A Variable Order Metric for DEDS Subject to Linear Invariants

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