The Model Counting Competition 2020

Fichte, Johannes Klaus; Hecher, Markus; Hamiti, Florim

doi:10.48550/arxiv.2012.01323

Cited by 2 publications

(2 citation statements)

References 34 publications

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“…Dynamic programming (DP) is widely used in Boolean reasoning problems such as satisfiability checking [20,21], Boolean synthesis [22], and model counting [23]. In practice, the DP-based model counter, ADDMC [24] tied for the first place in the weighted track of the 2020 Model Counting Competition [25]. Recently, ADDMC was further enhanced to DPMC [17] by decoupling the planning phase from the execution phase.…”

Section: Related Work Dynamic Programming and Maxsatmentioning

confidence: 99%

DPMS: An ADD-Based Symbolic Approach for Generalized MaxSAT Solving

Kyrillidis¹,

Vardi²,

Zhang³

2022

Preprint

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Boolean MaxSAT, as well as generalized formulations such as Min-MaxSAT and Max-hybrid-SAT, are fundamental optimization problems in Boolean reasoning. Existing methods for MaxSAT have been successful in solving benchmarks in CNF format. They lack, however, the ability to handle hybrid and generalized MaxSAT problems natively. To address this issue, we propose a novel dynamic-programming approach for solving generalized MaxSAT problems -called Dynamic-Programming-MaxSAT or DPMS for short-based on Algebraic Decision Diagrams (ADDs). With the power of ADDs and the (graded) project-join-tree builder, our versatile framework can handle many generalizations of MaxSAT, such as MaxSAT with non-CNF constraints, Min-MaxSAT and MinSAT. Moreover, DPMS scales provably well on instances with low width. Empirical results indicate that DPMS is able to solve certain problems quickly, where other algorithms based on various techniques all fail. Hence, DPMS is a promising framework and opens a new line of research that desires more investigation in the future.

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Section: Related Work Dynamic Programming and Maxsatmentioning

confidence: 99%

DPMS: An ADD-Based Symbolic Approach for Generalized MaxSAT Solving

Kyrillidis¹,

Vardi²,

Zhang³

2022

Preprint

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“…Another line of work focuses on compilation-based techniques, wherein the core approach is to compile the input formula into a subset L in negation normal form, so that counting is tractable for L. The past five years have witnessed a surge of interest in the design of projected model counters [6,18,20,42,45,52]. In this paper, we employ GANAK [52], the state of the art projected model counter; an entry based on GANAK won the projected model counting track at the 2020 model counting competition [31].…”

Section: Related Workmentioning

confidence: 99%

A Scalable Shannon Entropy Estimator

Golia

Juba

Meel

2022

Computer Aided Verification

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Quantified information flow (QIF) has emerged as a rigorous approach to quantitatively measure confidentiality; the information-theoretic underpinning of QIF allows the end-users to link the computed quantities with the computational effort required on the part of the adversary to gain access to desired confidential information. In this work, we focus on the estimation of Shannon entropy for a given program $$\varPi $$ Π . As a first step, we focus on the case wherein a Boolean formula $$\varphi (X,Y)$$ φ ( X , Y ) captures the relationship between inputs X and output Y of $$\varPi $$ Π . Such formulas $$\varphi (X,Y)$$ φ ( X , Y ) have the property that for every valuation to X, there exists exactly one valuation to Y such that $$\varphi $$ φ is satisfied. The existing techniques require $$\mathcal {O}(2^m)$$ O ( 2 m ) model counting queries, where $$m = |Y|$$ m = | Y | .We propose the first efficient algorithmic technique, called $$\mathsf {EntropyEstimation}$$ EntropyEstimation to estimate the Shannon entropy of $$\varphi $$ φ with PAC-style guarantees, i.e., the computed estimate is guaranteed to lie within a $$(1\pm \varepsilon )$$ ( 1 ± ε ) -factor of the ground truth with confidence at least $$1-\delta $$ 1 - δ . Furthermore, $$\mathsf {EntropyEstimation}$$ EntropyEstimation makes only $$\mathcal {O}(\frac{min(m,n)}{\varepsilon ^2})$$ O ( m i n ( m , n ) ε 2 ) counting and sampling queries, where $$m = |Y|$$ m = | Y | , and $$n = |X|$$ n = | X | , thereby achieving a significant reduction in the number of model counting queries. We demonstrate the practical efficiency of our algorithmic framework via a detailed experimental evaluation. Our evaluation demonstrates that the proposed framework scales to the formulas beyond the reach of the previously known approaches.

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The Model Counting Competition 2020

Cited by 2 publications

References 34 publications

DPMS: An ADD-Based Symbolic Approach for Generalized MaxSAT Solving

DPMS: An ADD-Based Symbolic Approach for Generalized MaxSAT Solving

A Scalable Shannon Entropy Estimator

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