On Computing the Union of MUSes

Mencía, Carlos; Kullmann, Oliver; Ignatiev, Alexey; Marques-Silva, João

doi:10.1007/978-3-030-24258-9_15

Cited by 17 publications

(10 citation statements)

References 29 publications

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“…The computation of the union UMUS F has been examined in two recent studies [13,45] that provided two different approaches for that task. Unfortunately, due to the problem's hardness, both the studies showed that the proposed approaches can usually handle only relatively small input formulas.…”

Section: W 3 -The Union Of Musesmentioning

confidence: 99%

“…While the early applications relied on identifying a single [3,6,7,51,53] or enumerating multiple [4,10,12,39,41,52] MUSes, the rapid adoption of MUSes lead researchers to investigate problem formulations and their corresponding applications that do not rely on explicit MUS identification. These include, e.g., computing the union of all MUSes [45], deciding whether a given clause belongs to an MUS [31], or counting the number of MUSes. Especially, the counting of MUSes found many applications in the domain of diagnosis where the MUS count can be used to compute various inconsistency metrics [25,29,[48][49][50]65] for general propositional knowledge bases.…”

Section: Introductionmentioning

confidence: 99%

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Counting Minimal Unsatisfiable Subsets

Bendík

Meel

2021

Computer Aided Verification

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Given an unsatisfiable Boolean formula F in CNF, an unsatisfiable subset of clauses U of F is called Minimal Unsatisfiable Subset (MUS) if every proper subset of U is satisfiable. Since MUSes serve as explanations for the unsatisfiability of F, MUSes find applications in a wide variety of domains. The availability of efficient SAT solvers has aided the development of scalable techniques for finding and enumerating MUSes in the past two decades. Building on the recent developments in the design of scalable model counting techniques for SAT, Bendík and Meel initiated the study of MUS counting techniques. They succeeded in designing the first approximate MUS counter, $$\mathsf {AMUSIC}$$ AMUSIC , that does not rely on exhaustive MUS enumeration. $$\mathsf {AMUSIC}$$ AMUSIC , however, suffers from two shortcomings: the lack of exact estimates and limited scalability due to its reliance on 3-QBF solvers.In this work, we address the two shortcomings of $$\mathsf {AMUSIC}$$ AMUSIC by designing the first exact MUS counter, $$\mathsf {CountMUST}$$ CountMUST , that does not rely on exhaustive enumeration. $$\mathsf {CountMUST}$$ CountMUST circumvents the need for 3-QBF solvers by reducing the problem of MUS counting to projected model counting. While projected model counting is #NP-hard, the past few years have witnessed the development of scalable projected model counters. An extensive empirical evaluation demonstrates that $$\mathsf {CountMUST}$$ CountMUST successfully returns MUS count for 1500 instances while $$\mathsf {AMUSIC}$$ AMUSIC and enumeration-based techniques could only handle up to 833 instances.

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Section: W 3 -The Union Of Musesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Counting Minimal Unsatisfiable Subsets

Bendík

Meel

2021

Computer Aided Verification

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“…The MUS-union problem was recently investigated by Mencia et al [ 42 ]. Their algorithm is based on gradually refining an under -approximation of until the exact is computed.…”

Section: Related Workmentioning

confidence: 99%

Approximate Counting of Minimal Unsatisfiable Subsets

Bendík

Meel

2020

Computer Aided Verification

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Given an unsatisfiable formula F in CNF, i.e. a set of clauses, the problem of Minimal Unsatisfiable Subset (MUS) seeks to identify a minimal subset of clauses such that N is unsatisfiable. The emerging viewpoint of MUSes as the root causes of unsatisfiability has led MUSes to find applications in a wide variety of diagnostic approaches. Recent advances in identification and enumeration of MUSes have motivated researchers to discover applications that can benefit from rich information about the set of MUSes. One such extension is that of counting the number of MUSes. The current best approach for MUS counting is to employ a MUS enumeration algorithm, which often does not scale for the cases with a reasonably large number of MUSes. Motivated by the success of hashing-based techniques in the context of model counting, we design the first approximate MUS counting procedure with guarantees, called . Our approach avoids exhaustive MUS enumeration by combining the classical technique of universal hashing with advances in QBF solvers along with a novel usage of union and intersection of MUSes to achieve runtime efficiency. Our prototype implementation of is shown to scale to instances that were clearly beyond the realm of enumeration-based approaches.

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“…Luo et al [19] proposed a method for accelerating the enumeration of MUSes based on inconsistency graph partitioning. A novel algorithm [20] is presented for computing the union of the clauses included in some MUSes, by developing a refined recursive enumeration of MUSes based on powerful pruning techniques.…”

Section: Algorithms Of Extracting Unsatisfiable Subformulamentioning

confidence: 99%

FPGA Routing Acceleration by Extracting Unsatisfiable Subformulas

Zhang¹,

Li²,

Ma³

2020

Computer Science &Amp; Information Technology (CS &Amp; IT)

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Explaining the causes of infeasibility of Boolean formulas has practical applications in various fields. A small unsatisfiable subset can provide a succinct explanation of infeasibility and is valuable for applications, such as FPGA routing. The Boolean-based FPGA detailed routing formulation expresses the routing constraints as a Boolean function which is satisfiable if and only if the layout is routable. The unsatisfiable subformulas can help the FPGA routing tool to diagnose and eliminate the causes of unroutable. For this typical application, a resolutionbased local search algorithm to extract unsatisfiable subformulas is integrated into Booleanbased FPGA routing method. The fastest algorithm of deriving minimum unsatisfiable subformulas, called the branch-and-bound algorithm, is adopted to compare with the local search algorithm. On the standard FPGA routing benchmark, the results show that the local search algorithm outperforms the branch-and-bound algorithm on runtime. It is also concluded that the unsatisfiable subformulas play a very important role in FPGA routing real applications.

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On Computing the Union of MUSes

Cited by 17 publications

References 29 publications

Counting Minimal Unsatisfiable Subsets

Counting Minimal Unsatisfiable Subsets

Approximate Counting of Minimal Unsatisfiable Subsets

FPGA Routing Acceleration by Extracting Unsatisfiable Subformulas

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