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

Abstract

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.

Presentation of the 9th Edition of the Model Checking Contest

“…This last estimate is extracted from the basis of the P-flows. The i Rank metric shows very high correlation between its value and the final MDD size: on a test benchmark [4] i Rank got a correlation of 0.96, while the previously best known metrics (SOUPS and PTS) had a correlation of 0.77 and 0.67, respectively. As a consequence, GreatSPN should have a very high chance of taking a good variable order as a first guess for a very large number of models.…”

“…Over the last years we collected a large experience in variable order evaluation, which ended in the design of a new highly correlating metric [4] called i Rank that will be used in the MCC'2019.…”

“…https://github.com/tvtaqa/enPAC. 3 https://github.com/greatspn/SOURCES 4. NUPN[22] stands for Nested Unit Petri Nets, this is a way to carry out structural and hierarchical information about the structure of the modeled system.…”

starMC: an automata based CTL* model checker

“…R2 : the approach of R1 is any better than a translation to μ -calculus? R3 : variable ordering techniques that exploits the PN structure, like the ones developed in Amparore et al (2019) for state-space exploration, can be successfully applied to CTL model-checking? R4 : can a Büchi-based approach favour the formulation of counterexamples and witnesses?…”

A CTL* Model Checker for Petri Nets

“…We undertook the construction of a CTL* model checker to use it: 1) to test the efficiency of a DD-based implementation of LTL and CTL*; 2) to explore whether a Büchi automata approach can favour the formulation of counterexamples and witnesses; 3) to investigate the efficacy for CTL* of the variable ordering techniques developed in [3]; and 4) to support teaching: following the effort in [4] the users of GreatSPN to experiment (within the same window of the GUI) formulae of multiple logics: LTL, (fair )CTL and CTL*.…”