PBLib – A Library for Encoding Pseudo-Boolean Constraints into CNF

Philipp, Tobias; Steinke, Peter

doi:10.1007/978-3-319-24318-4_2

Cited by 42 publications

(26 citation statements)

References 19 publications

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“…We have implemented the adder encoder and the BDD encoders in the Pi-catSAT compiler [22], and have compared these encoders on three sets of benchmarks. While theoretical studies have ruled out the adder encoding as viable due to its incapability of maintaining GAC (Generalized Arc Consistency) on PB constraints, and past empirical studies have unanimously confirmed its poor performance [1,13,16], our experiments revealed surprisingly good and consistent performance of the optimized adder encoder in comparison with the BDD and other encoders.…”

Section: Introductionmentioning

confidence: 57%

“…The benchmarks are available at http://picat-lang.org/download/pb bench.tar.gz. We also included PBSugar (version 1.1.1) [19] and PBLib [16], 6 two cutting-edge PB encoders, in the comparison on the PB'16 benchmarks, and Chuffed 7 , a cutting- edge solver that integrates SAT and CP solving techniques, in the comparison on cumulative scheduling. We did the experiment on Linux Ubuntu with an Intel i7 3.30GHz CPU and 32GB RAM, and used the SAT solvers Glucose (version 4.1) 8 and Lingeling (version 587f) 9 in the experiments.…”

Section: Resultsmentioning

confidence: 99%

“…BDDs (Binary Decision Diagrams) have been used as an intermediate form for translating PB constraints into SAT [1,13,16]. A node N in a BDD represents a constraint.…”

Section: Encoding Bdds Into Satmentioning

confidence: 99%

See 2 more Smart Citations

Encoding PB Constraints into SAT via Binary Adders and BDDs -- Revisited

Zhou¹,

Kjellerstrand²

2018

EasyChair Preprints

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Pseudo-Boolean constraints constitute an important class of constraints. Despite extensive studies of SAT encodings for PB constraints, there are no generally accepted SAT encodings for PB constraints. In this paper we revisit encoding PB constraints into SAT via binary adders and BDDs. For the binary adder encoding, we present an optimizing compiler that incorporates preprocessing, decomposition, constant propagation, and common subexpression elimination techniques tailored to PB constraints. For encoding via BDDs, we compare three methods for converting BDDs into SAT, namely, path encoding, 6-clause node encoding, and 2-clause node encoding. We experimentally compare these encodings on three sets of benchmarks. Our experiments revealed surprisingly good and consistent performance of the optimized adder encoder in comparison with other encoders.

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Section: Introductionmentioning

confidence: 57%

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Encoding PB Constraints into SAT via Binary Adders and BDDs -- Revisited

Zhou¹,

Kjellerstrand²

2018

EasyChair Preprints

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“…We use the PyTorch (v1.0.1.post2) [79] deep learning platform to train and test binarized neural networks. For encoding the BNNs to CNF, we build our own tool using the PBLib library [81] for encoding the cardinality constraints to CNF. The resulting CNF formula is annotated with a projection set and NPAQ invokes the approximate model counter ApproxMC3 [92] to count the number of solutions.…”

Section: Implementation and Evaluationmentioning

confidence: 99%

Quantitative Verification of Neural Networks and Its Security Applications

Baluta

Shen

Shinde

et al. 2019

Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security

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Neural networks are increasingly employed in safety-critical domains. This has prompted interest in verifying or certifying logically encoded properties of neural networks. Prior work has largely focused on checking existential properties, wherein the goal is to check whether there exists any input that violates a given property of interest. However, neural network training is a stochastic process, and many questions arising in their analysis require probabilistic and quantitative reasoning, i.e., estimating how many inputs satisfy a given property. To this end, our paper proposes a novel and principled framework to quantitative verification of logical properties specified over neural networks. Our framework is the first to provide PAC-style soundness guarantees, in that its quantitative estimates are within a controllable and bounded error from the true count. We instantiate our algorithmic framework by building a prototype tool called NPAQ that enables checking rich properties over binarized neural networks. We show how emerging security analyses can utilize our framework in 3 concrete point applications: quantifying robustness to adversarial inputs, efficacy of trojan attacks, and fairness/bias of given neural networks.

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“…First is the PBLIB ver. 1.2.1, by Tobias Philipp and Peter Steinke [19]. This solver implements a plethora of encodings for three types of constraints: at-most-one, atmost-k (cardinality constraints) and Pseudo-Boolean constraints.…”

Section: Encodingsmentioning

confidence: 99%

Encoding cardinality constraints using multiway merge selection networks

Karpiński

Piotrów

2019

Constraints

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Boolean cardinality constraints (CCs) state that at most (at least, or exactly) k out of n propositional literals can be true. We propose a new, arc-consistent, easy to implement and efficient encoding of CCs based on a new class of selection networks. Several comparator networks have been recently proposed for encoding CCs and experiments have proved their efficiency (Abío et al. 2013, Asín et al. Constraints 12(2): 195-221, 2011, Codish and Zazon-Ivry 2010, Eén and Sörensson Boolean Modeling and Computation 2: 1 -26, 2006). In our construction we use the idea of the multiway merge sorting networks by Lee and Batcher (1995) that generalizes the technique of odd-even sorting ones by merging simultaneously more than two subsequences. The new selection network merges 4 subsequences in that way. Based on this construction, we can encode more efficiently comparators in the combine phase of the network: instead of encoding each comparator separately by 3 clauses and 2 additional variables, we propose an encoding scheme that requires 5 clauses and 2 variables on average for each pair of comparators. We also extend the model of comparator networks so that the basic components are not only comparators (2-sorters) but more general m-sorters, for m ∈ {2, 3, 4}, that can also be encoded efficiently. We show that with small overhead (regarding implementation complexity) we can achieve a significant improvement in SAT-solver runtime for many test cases. We prove that the new encoding is competitive to the other state-of-the-art encodings.

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PBLib – A Library for Encoding Pseudo-Boolean Constraints into CNF

Cited by 42 publications

References 19 publications

Encoding PB Constraints into SAT via Binary Adders and BDDs -- Revisited

Encoding PB Constraints into SAT via Binary Adders and BDDs -- Revisited

Quantitative Verification of Neural Networks and Its Security Applications

Encoding cardinality constraints using multiway merge selection networks

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