Accelerated Deletion-based Extraction of Minimal Unsatisfiable Cores

Nadel, Alexander; Ryvchin, Vadim; Strichman, Ofer

doi:10.3233/sat190100

Cited by 16 publications

(15 citation statements)

References 46 publications

(69 reference statements)

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“…However, some constraint domains might enjoy domain specific properties that allow to shrink the seed very efficiently, regardless of the size of the seed. In particular, the CNF form of Boolean (SAT) formulas allows to significantly reduce the number of performed satisfiability checks [8,32,6]. Finally, the reduction of the search space is driven by previously found MUSes.…”

Section: Discussionmentioning

confidence: 99%

Recursive Online Enumeration of All Minimal Unsatisfiable Subsets

Bendík

Černá

Beneš

2018

Automated Technology for Verification and Analysis

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In various areas of computer science, we deal with a set of constraints to be satisfied. If the constraints cannot be satisfied simultaneously, it is desirable to identify the core problems among them. Such cores are called minimal unsatisfiable subsets (MUSes). The more MUSes are identified, the more information about the conflicts among the constraints is obtained. However, a full enumeration of all MUSes is in general intractable due to the large number (even exponential) of possible conflicts. Moreover, to identify MUSes, algorithms have to test sets of constraints for their simultaneous satisfiability. The type of the test depends on the application domains. The complexity of the tests can be extremely high especially for domains like temporal logics, model checking, or SMT. In this paper, we propose a recursive algorithm that identifies MUSes in an online manner (i.e., one by one) and can be terminated at any time. The key feature of our algorithm is that it minimises the number of satisfiability tests and thus speeds up the computation. The algorithm is applicable to an arbitrary constraint domain and its effectiveness demonstrates itself especially in domains with expensive satisfiability checks. We benchmark our algorithm against the state-of-the-art algorithm Marco on the Boolean and SMT constraint domains and demonstrate that our algorithm really requires less satisfiability tests and consequently finds more MUSes in the given time limits.

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Section: Discussionmentioning

confidence: 99%

Recursive Online Enumeration of All Minimal Unsatisfiable Subsets

Bendík

Černá

Beneš

2018

Automated Technology for Verification and Analysis

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“…Our method for computing all MIVCs was inspired by recent work in the domain of satisfiability analysis [55]. One interesting future direction is to devise similar MIVC enumeration algorithms based on other studies on MUSes extraction such as [54]. Another interesting direction for this project is to parallelize the enumeration process: it is certainly possible to ask for multiple distinct maximal models to be solved in parallel.…”

Section: Future Research Directionsmentioning

confidence: 99%

Inductive Validity Cores

Ghassabani

Whalen

Gacek

et al. 2021

IIEEE Trans. Software Eng.

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Symbolic model checkers can construct proofs of properties over very complex models. However, the results reported by the tool when a proof succeeds do not generally provide much insight to the user. It is often useful for users to have traceability information related to the proof: which portions of the model were necessary to construct it. This traceability information can be used to diagnose a variety of modeling problems such as overconstrained axioms and underconstrained properties, and can also be used to measure completeness of a set of requirements over a model. We propose the notion of inductive validity cores (IVCs), which are intended to trace a property to a minimal set of model elements necessary for proof. Such cores are not unique, and algorithms for efficiently producing both single IVC and all IVCs are presented. IVCs can be used for several interesting analyses, including regression analysis for testing/proof, determination of the minimum (as opposed to minimal) number of model elements necessary for proof, the diversity examination of model elements leading to proof, and analyzing fault tolerance.

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“…Domain specific algorithms (e.g. [5,24,1,19]) that are based on Algorithm 1 are often able to further reduce the number of performed satisfiability checks by exploiting domain specific properties of particular constraint domains.…”

Section: Shrinkmentioning

confidence: 99%

MUST: Minimal Unsatisfiable Subsets Enumeration Tool

Bendík

Černá

2020

Lecture Notes in Computer Science

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In many areas of computer science, we are given an unsatisfiable set of constraints with the goal to provide an insight into the unsatisfiability. One of common approaches is to identify minimal unsatisfiable subsets (MUSes) of the constraint set. The more MUSes are identified, the better insight is obtained. However, since there can be up to exponentially many MUSes, their complete enumeration might be intractable. Therefore, we focus on algorithms that enumerate MUSes online, i.e. one by one, and thus can find at least some MUSes even in the intractable cases. Since MUSes find applications in different constraint domains and new applications still arise, there have been proposed several domain agnostic algorithms. Such algorithms can be applied in any constraint domain and thus theoretically serve as ready-to-use solutions for all the emerging applications. However, there are almost no domain agnostic tools, i.e. tools that both implement domain agnostic algorithms and can be easily extended to support any constraint domain. In this work, we close this gap by introducing a domain agnostic tool called MUST. Our tool outperforms other existing domain agnostic tools and moreover, it is even competitive to fully domain specific solutions.

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Accelerated Deletion-based Extraction of Minimal Unsatisfiable Cores

Cited by 16 publications

References 46 publications

Recursive Online Enumeration of All Minimal Unsatisfiable Subsets

Recursive Online Enumeration of All Minimal Unsatisfiable Subsets

Inductive Validity Cores

MUST: Minimal Unsatisfiable Subsets Enumeration Tool

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