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Mate Soos

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11 papers

2 author rows

SAT Conference 2025 Conference Paper

Efficient Certified Reasoning for Binarized Neural Networks

Jiong Yang 0002
Yong Kiam Tan
Mate Soos
Magnus O. Myreen
Kuldeep S. Meel

Neural networks have emerged as essential components in safety-critical applications - these use cases demand complex, yet trustworthy computations. Binarized Neural Networks (BNNs) are a type of neural network where each neuron is constrained to a Boolean value; they are particularly well-suited for safety-critical tasks because they retain much of the computational capacities of full-scale (floating-point or quantized) deep neural networks, but remain compatible with satisfiability solvers for qualitative verification and with model counters for quantitative reasoning. However, existing methods for BNN analysis suffer from either limited scalability or susceptibility to soundness errors, which hinders their applicability in real-world scenarios. In this work, we present a scalable and trustworthy approach for both qualitative and quantitative verification of BNNs. Our approach introduces a native representation of BNN constraints in a custom-designed solver for qualitative reasoning, and in an approximate model counter for quantitative reasoning. We further develop specialized proof generation and checking pipelines with native support for BNN constraint reasoning, ensuring trustworthiness for all of our verification results. Empirical evaluations on a BNN robustness verification benchmark suite demonstrate that our certified solving approach achieves a 9× speedup over prior certified CNF and PB-based approaches, and our certified counting approach achieves a 218× speedup over the existing CNF-based baseline. In terms of coverage, our pipeline produces fully certified results for 99% and 86% of the qualitative and quantitative reasoning queries on BNNs, respectively. This is in sharp contrast to the best existing baselines which can fully certify only 62% and 4% of the queries, respectively.

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SAT Conference 2023 Conference Paper

Algorithms Transcending the SAT-Symmetry Interface

Markus Anders
Pascal Schweitzer
Mate Soos

Dedicated treatment of symmetries in satisfiability problems (SAT) is indispensable for solving various classes of instances arising in practice. However, the exploitation of symmetries usually takes a black box approach. Typically, off-the-shelf external, general-purpose symmetry detection tools are invoked to compute symmetry groups of a formula. The groups thus generated are a set of permutations passed to a separate tool to perform further analyzes to understand the structure of the groups. The result of this second computation is in turn used for tasks such as static symmetry breaking or dynamic pruning of the search space. Within this pipeline of tools, the detection and analysis of symmetries typically incurs the majority of the time overhead for symmetry exploitation. In this paper we advocate for a more holistic view of what we call the SAT-symmetry interface. We formulate a computational setting, centered around a new concept of joint graph/group pairs, to analyze and improve the detection and analysis of symmetries. Using our methods, no information is lost performing computational tasks lying on the SAT-symmetry interface. Having access to the entire input allows for simpler, yet efficient algorithms. Specifically, we devise algorithms and heuristics for computing finest direct disjoint decompositions, finding equivalent orbits, and finding natural symmetric group actions. Our algorithms run in what we call instance-quasi-linear time, i. e. , almost linear time in terms of the input size of the original formula and the description length of the symmetry group returned by symmetry detection tools. Our algorithms improve over both heuristics used in state-of-the-art symmetry exploitation tools, as well as theoretical general-purpose algorithms.

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IJCAI Conference 2023 Conference Paper

Engineering an Efficient Approximate DNF-Counter

Mate Soos
Divesh Aggarwal
Sourav Chakraborty
Kuldeep S. Meel
Maciej Obremski

Model counting is a fundamental problem with many practical applications, including query evaluation in probabilistic databases and failure-probability estimation of networks. In this work, we focus on a variant of this problem where the underlying formula is expressed in Disjunctive Normal Form (DNF), also known as #DNF. This problem has been shown to be #P-complete, making it intractable to solve exactly. Much research has therefore been focused on obtaining approximate solutions, particularly in the form of (epsilon, delta) approximations. The primary contribution of this paper is a new approach, called pepin, to approximate #DNF counting that achieves (nearly) optimal time complexity and outperforms existing FPRAS. Our approach is based on the recent breakthrough in the context of union of sets in streaming. We demonstrate the effectiveness of our approach through extensive experiments and show that it provides an affirmative answer to the challenge of efficiently computing #DNF.

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SAT Conference 2023 Conference Paper

Explaining SAT Solving Using Causal Reasoning

Jiong Yang 0002
Arijit Shaw
Teodora Baluta
Mate Soos
Kuldeep S. Meel

The past three decades have witnessed notable success in designing efficient SAT solvers, with modern solvers capable of solving industrial benchmarks containing millions of variables in just a few seconds. The success of modern SAT solvers owes to the widely-used CDCL algorithm, which lacks comprehensive theoretical investigation. Furthermore, it has been observed that CDCL solvers still struggle to deal with specific classes of benchmarks comprising only hundreds of variables, which contrasts with their widespread use in real-world applications. Consequently, there is an urgent need to uncover the inner workings of these seemingly weak yet powerful black boxes. In this paper, we present a first step towards this goal by introducing an approach called {CausalSAT}, which employs causal reasoning to gain insights into the functioning of modern SAT solvers. {CausalSAT} initially generates observational data from the execution of SAT solvers and learns a structured graph representing the causal relationships between the components of a SAT solver. Subsequently, given a query such as whether a clause with low literals blocks distance (LBD) has a higher clause utility, {CausalSAT} calculates the causal effect of LBD on clause utility and provides an answer to the question. We use {CausalSAT} to quantitatively verify hypotheses previously regarded as "rules of thumb" or empirical findings, such as the query above or the notion that clauses with high LBD experience a rapid drop in utility over time. Moreover, {CausalSAT} can address previously unexplored questions, like which branching heuristic leads to greater clause utility in order to study the relationship between branching and clause management. Experimental evaluations using practical benchmarks demonstrate that {CausalSAT} effectively fits the data, verifies four "rules of thumb", and provides answers to three questions closely related to implementing modern solvers.

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KR Conference 2021 Conference Paper

Gaussian Elimination Meets Maximum Satisfiability

Mate Soos
Kuldeep S. Meel

Given a set of constraints F and a weight function W over the assignments, the problem of MaxSAT is to compute a maximum weighted solution of F. MaxSAT is a fundamental problem with applications in numerous areas. The success of MaxSAT solvers has prompted researchers in AI and formal methods communities to develop algorithms that can use MaxSAT solver as oracle. One such problem that stands to benefit from advances in MaxSAT solving is discrete integration. Recently, Ermon et al. achieved a significant breakthrough by reducing the problem of integration to polynomially many queries to an optimization oracle where $F$ is conjuncted with randomly chosen XOR constraints. Unlike approximate model counting, where hashing-based approaches have been able to achieve scalability as well as rigorous formal guarantees, the practical evaluation of Ermon et al's approach, called WISH, often sacrifice theoretical guarantees, largely due to lack of existing MaxSAT solvers with native XOR support. The primary contribution of this paper is a new MaxSAT solver, GaussMaxHS, with built-in XOR support. The architecture of GaussMaxHS is inspired by CryptoMiniSAT, which has been the workhorse of hashing-based approximate model counting techniques. The resulting solver, GaussMaxHS, outperforms MaxHS over 9628 benchmarks arising from spin glass models and network reliability domains. In particular, with a timeout of 5000 seconds, MaxHS could solve only 5473 benchmarks while GaussMaxHS could solve 6120 benchmarks.

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SAT Conference 2021 Conference Paper

Leveraging GPUs for Effective Clause Sharing in Parallel SAT Solving

Nicolas Prevot
Mate Soos
Kuldeep S. Meel

Abstract The past two decades have witnessed an unprecedented improvement in runtime performance of SAT solvers owing to clever software engineering and creative design of data structures. Yet, most entries in the annual SAT competition retain the core architecture of MiniSat, which was designed from the perspective of single core CPU architectures. Since 2005, however, there has been a significant shift to heterogeneous architectures owing to the impending end of Dennard scaling. The primary contribution of this work is a novel multi-threaded CDCL-based framework, called $\mathsf {GPUShareSat}$, designed to take advantage of CPU+GPU architectures. The core underlying principle of our approach is to divide the tasks among the CPU and the GPU so as to attempt to achieve the best of both worlds. We observe that bit-vector based operations can allow a GPU to efficiently determine the usefulness of a learnt clause to different threads and accordingly notify the thread of the presence of relevant clauses. This approach of checking all clauses against all assignments from different threads allows the GPU to exploit its potential for massive parallelism through clever group-testing strategy and bitwise operations. Our detailed empirical analysis shows practical efficiency of our approach: in particular, $\mathsf {GPUShareSat}$ augmented with the state-of-the-art single-threaded solver Relaxed_LCMDCBDL_newTech solved 19 more instances than the winner of the 2020 SAT competition’s parallel track, P-MCOMSPS-STR.

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AAAI Conference 2019 Conference Paper

BIRD: Engineering an Efficient CNF-XOR SAT Solver and Its Applications to Approximate Model Counting

Mate Soos
Kuldeep S. Meel

Given a Boolean formula φ, the problem of model counting, also referred to as #SAT is to compute the number of solutions of φ. Model counting is a fundamental problem in artificial intelligence with a wide range of applications including probabilistic reasoning, decision making under uncertainty, quantified information flow, and the like. Motivated by the success of SAT solvers, there has been surge of interest in the design of hashing-based techniques for approximate model counting for the past decade. We profiled the state of the art approximate model counter ApproxMC2 and observed that over 99. 99% of time is consumed by the underlying SAT solver, CryptoMiniSat. This observation motivated us to ask: Can we design an efficient underlying CNF-XOR SAT solver that can take advantage of the structure of hashing-based algorithms and would this lead to an efficient approximate model counter? The primary contribution of this paper is an affirmative answer to the above question. We present a novel architecture, called BIRD, to handle CNF-XOR formulas arising from hashingbased techniques. The resulting hashing-based approximate model counter, called ApproxMC3, employs the BIRD framework in its underlying SAT solver, CryptoMiniSat. To the best of our knowledge, we conducted the most comprehensive study of evaluation performance of counting algorithms involving 1896 benchmarks with computational effort totaling 86400 computational hours. Our experimental evaluation demonstrates significant runtime performance improvement for ApproxMC3 over ApproxMC2. In particular, we solve 648 benchmarks more than ApproxMC2, the state of the art approximate model counter and for all the formulas where both ApproxMC2 and ApproxMC3 did not timeout and took more than 1 seconds, the mean speedup is 284. 40 – more than two orders of magnitude.

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SAT Conference 2019 Conference Paper

CrystalBall: Gazing in the Black Box of SAT Solving

Mate Soos
Raghav Kulkarni
Kuldeep S. Meel

Abstract Boolean satisfiability is a fundamental problem in computer science with a wide range of applications including planning, configuration management, design and verification of software/hardware systems. The annual SAT competition continues to witness impressive improvements in the performance of the winning SAT solvers largely thanks to the development of new heuristics arising out of intensive collaborative research in the SAT community. Modern SAT solvers achieve scalability and robustness with sophisticated heuristics that are challenging to understand and explain. Consequently, the development of new algorithmic insights has been primarily restricted to expert intuitions and evaluation of the new insights have been restricted to performance measurement in terms of the runtime of solvers or a proxy for the runtime of solvers. In this context, one may ask: whether it is possible to develop a framework to provide white-box access to the execution of SAT solver that can aid both SAT solver developers and users to synthesize algorithmic heuristics for modern SAT solvers? The primary focus of our project is precisely such a framework, which we call $\mathsf {CrystalBall}$. More precisely, we propose to view modern conflict-driven clause learning ( $\mathsf {CDCL}$ ) solvers as a composition of classifiers and regressors for different tasks such as branching, clause memory management, and restarting. The primary objective of this paper is to introduce a framework to peek inside the SAT solvers – $\mathsf {CrystalBall}$ – to the AI and SAT community. The current version of $\mathsf {CrystalBall}$ focuses on deriving a classifier to keep or throw away a learned clause. In a departure from recent machine learning based techniques, $\mathsf {CrystalBall}$ employs supervised learning and uses extensive, multi-gigabyte data extracted from runs of a single SAT solver to perform predictive analytics.

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IJCAI Conference 2019 Conference Paper

GANAK: A Scalable Probabilistic Exact Model Counter

Shubham Sharma
Subhajit Roy
Mate Soos
Kuldeep S. Meel

Given a Boolean formula F, the problem of model counting, also referred to as #SAT, seeks to compute the number of solutions of F. Model counting is a fundamental problem with a wide variety of applications ranging from planning, quantified information flow to probabilistic reasoning and the like. The modern #SAT solvers tend to be either based on static decomposition, dynamic decomposition, or a hybrid of the two. Despite dynamic decomposition based #SAT solvers sharing much of their architecture with SAT solvers, the core design and heuristics of dynamic decomposition-based #SAT solvers has remained constant for over a decade. In this paper, we revisit the architecture of the state-of-the-art dynamic decomposition-based #SAT tool, sharpSAT, and demonstrate that by introducing a new notion of probabilistic component caching and the usage of universal hashing for exact model counting along with the development of several new heuristics can lead to significant performance improvement over state-of-the-art model-counters. In particular, we develop GANAK, a new scalable probabilistic exact model counter that outperforms state-of-the-art exact and approximate model counters sharpSAT and ApproxMC3 respectively, both in terms of PAR-2 score and the number of instances solved. Furthermore, in our experiments, the model count returned by GANAK was equal to the exact model count for all the benchmarks. Finally, we observe that recently proposed preprocessing techniques for model counting benefit exact model counters while hurting the performance of approximate model counters.

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SAT Conference 2012 Conference Paper

Lynx: A Programmatic SAT Solver for the RNA-Folding Problem

Vijay Ganesh 0001
Charles W. O'Donnell
Mate Soos
Srinivas Devadas
Martin C. Rinard
Armando Solar-Lezama

Abstract This paper introduces Lynx, an incremental programmatic SAT solver that allows non-expert users to introduce domain-specific code into modern conflict-driven clause-learning (CDCL) SAT solvers, thus enabling users to guide the behavior of the solver. The key idea of Lynx is a callback interface that enables non-expert users to specialize the SAT solver to a class of Boolean instances. The user writes specialized code for a class of Boolean formulas, which is periodically called by Lynx’s search routine in its inner loop through the callback interface. The user-provided code is allowed to examine partial solutions generated by the solver during its search, and to respond by adding CNF clauses back to the solver dynamically and incrementally. Thus, the user-provided code can specialize and influence the solver’s search in a highly targeted fashion. While the power of incremental SAT solvers has been amply demonstrated in the SAT literature and in the context of DPLL(T), it has not been previously made available as a programmatic API that is easy to use for non-expert users. Lynx’s callback interface is a simple yet very effective strategy that addresses this need. We demonstrate the benefits of Lynx through a case-study from computational biology, namely, the RNA secondary structure prediction problem. The constraints that make up this problem fall into two categories: structural constraints, which describe properties of the biological structure of the solution, and energetic constraints, which encode quantitative requirements that the solution must satisfy. We show that by introducing structural constraints on-demand through user provided code we can achieve, in comparison with standard SAT approaches, upto 30x reduction in memory usage and upto 100x reduction in time.

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SAT Conference 2009 Conference Paper

Extending SAT Solvers to Cryptographic Problems

Mate Soos
Karsten Nohl
Claude Castelluccia

Abstract Cryptography ensures the confidentiality and authenticity of information but often relies on unproven assumptions. SAT solvers are a powerful tool to test the hardness of certain problems and have successfully been used to test hardness assumptions. This paper extends a SAT solver to efficiently work on cryptographic problems. The paper further illustrates how SAT solvers process cryptographic functions using automatically generated visualizations, introduces techniques for simplifying the solving process by modifying cipher representations, and demonstrates the feasibility of the approach by solving three stream ciphers. To optimize a SAT solver for cryptographic problems, we extended the solver’s input language to support the XOR operation that is common in cryptography. To better understand the inner workings of the adapted solver and to identify bottlenecks, we visualize its execution. Finally, to improve the solving time significantly, we remove these bottlenecks by altering the function representation and by pre-parsing the resulting system of equations. The main contribution of this paper is a new approach to solving cryptographic problems by adapting both the problem description and the solver synchronously instead of tweaking just one of them. Using these techniques, we were able to solve a well-researched stream cipher 2 6 times faster than was previously possible.

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