Using Minimal Correction Sets to More Efficiently Compute Minimal Unsatisfiable Sets

Bacchus, Fahiem; Katsirelos, George

doi:10.1007/978-3-319-21668-3_5

Cited by 26 publications

(26 citation statements)

References 20 publications

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“…Many modern shrinking algorithms [2,8,31] use critical constraints to speed up their computation. Every MUS of C has to contain all the critical constraints for C and this helps the shrinking procedure to narrow the search space.…”

Section: Algorithmmentioning

confidence: 99%

“…The list of existing approaches to the MUS enumeration problem is short, especially compared to the amount of work dealing with a single MUS extraction [6,7,8,9,30,32]. Moreover, existing algorithms for the MUS enumeration are tailored mainly to Boolean constraints [21,23,3,2] and cannot be applied to other constraints. The approaches that focus on MUS enumeration in general constraint systems can be divided into two categories: approaches that compute MUSes directly and those that rely on the hitting set duality.…”

Section: Related Workmentioning

confidence: 99%

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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: Algorithmmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Recursive Online Enumeration of All Minimal Unsatisfiable Subsets

Bendík

Černá

Beneš

2018

Automated Technology for Verification and Analysis

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“…There are several algorithms that were tailored to a particular constraint domain. Algorithms MCS-MUS-ALL [2], MCS-MUS-ALL-BT [3], and Grow-Shrink [13] are based on a domain agnostic relationship between MUSes and MCSes. However, the core procedures of these algorithms are efficient only due to exploiting specific properties of their particular constraint domains (the conjunctive normal form of Boolean formulas, model checking properties).…”

Section: Evaluated Algorithmsmentioning

confidence: 99%

“…The problem of MUS identification was extensively studied in the past decades [8,7,31,2,29,4,11,13,32]. The existing solutions can be divided into two categories: identification of a single MUS, and enumeration of all MUSes.…”

Section: Introductionmentioning

confidence: 99%

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Evaluation of Domain Agnostic Approaches for Enumeration of Minimal Unsatisfiable Subsets

Bendík¹,

Černá²

EPiC Series in Computing

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In many different applications we are given a set of constraints with the goal to decide whether the set is satisfiable. If the set is determined to be unsatisfiable, one might be interested in analysing this unsatisfiability. Identification of minimal unsatisfiable subsets (MUSes) is a kind of such analysis. The more MUSes are identified, the better insight into the unsatisfiability is obtained. However, the full enumeration of all MUSes is often intractable. Therefore, algorithms that identify MUSes in an online fashion, i.e., one by one, are needed. Moreover, since MUSes find applications in various constraint domains, and new applications still arise, there is a desire for domain agnostic MUS enumeration approaches.In this paper, we present an experimental evaluation of four state-of-the-art domain agnostic MUS enumeration algorithms: MARCO, TOME, ReMUS, and DAA. The evalu- ation is conducted in the SAT, SMT, and LTL constraint domains. The results evidence that there is no silver-bullet algorithm that would beat all the others in all the domains.

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Speeding Up Assumption-Based SAT

Hickey

Bacchus

2019

Lecture Notes in Computer Science

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Using Minimal Correction Sets to More Efficiently Compute Minimal Unsatisfiable Sets

Cited by 26 publications

References 20 publications

Recursive Online Enumeration of All Minimal Unsatisfiable Subsets

Recursive Online Enumeration of All Minimal Unsatisfiable Subsets

Evaluation of Domain Agnostic Approaches for Enumeration of Minimal Unsatisfiable Subsets

Speeding Up Assumption-Based SAT

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