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  • 1. Ansotegui, Carlos
    et al.
    Luisa Bonet, Maria
    Giraldez-Cru, Jesus
    KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS. Spanish National Research Council, Spain.
    Levy, Jordi
    Structure features for SAT instances classification2017In: Journal of Applied Logic, ISSN 1570-8683, E-ISSN 1570-8691, Vol. 23, p. 27-39Article in journal (Refereed)
    Abstract [en]

    The success of portfolio approaches in SAT solving relies on the observation that different SAT solvers may dramatically change their performance depending on the class of SAT instances they are trying to solve. In these approaches, a set of features of the problem is used to build a prediction model, which classifies instances into classes, and computes the fastest algorithm to solve each of them. Therefore, the set of features used to build these classifiers plays a crucial role. Traditionally, portfolio SAT solvers include features about the structure of the problem and its hardness. Recently, there have been some attempts to better characterize the structure of industrial SAT instances. In this paper, we use some structure features of industrial SAT instances to build some classifiers of industrial SAT families of instances. Namely, they are the scale-free structure, the community structure and the self similar structure. First, we measure the effectiveness of these classifiers by comparing them to other sets of SAT features commonly used in portfolio SAT solving approaches. Then, we evaluate the performance of this set of structure features when used in a real portfolio SAT solver. Finally, we analyze the relevance of these features on the analyzed classifiers.

  • 2. Baud-Berthier, G.
    et al.
    Giráldez-Cru, Jesús
    KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.
    Simon, L.
    On the community structure of bounded model checking SAT problems2017In: 20th International Conference on Theory and Applications of Satisfiability Testing, SAT 2017, Springer, 2017, Vol. 10491, p. 65-82Conference paper (Refereed)
    Abstract [en]

    Following the impressive progress made in the quest for efficient SAT solving in the last years, a number of researches has focused on explaining performances observed on typical application problems. However, until now, tentative explanations were only partial, essentially because the semantic of the original problem was lost in the translation to SAT. In this work, we study the behavior of so called “modern” SAT solvers under the prism of the first successful application of CDCL solvers, i.e., Bounded Model Checking. We trace the origin of each variable w.r.t. its unrolling depth, and show a surprising relationship between these time steps and the communities found in the CNF encoding. We also show how the VSIDS heuristic, the resolution engine, and the learning mechanism interact with the unrolling steps. Additionally, we show that the Literal Block Distance (LBD), used to identify good learnt clauses, is related to this measure. Our work shows that communities identify strong dependencies among the variables of different time steps, revealing a structure that arises when unrolling the problem, and which seems to be caught by the LBD measure.

  • 3.
    Elffers, Jan
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Theoretical Computer Science, TCS.
    Giráldez-Cru, Jakob
    KTH, School of Electrical Engineering and Computer Science (EECS), Theoretical Computer Science, TCS.
    Nordström, Jakob
    KTH, School of Electrical Engineering and Computer Science (EECS), Theoretical Computer Science, TCS.
    Vinyals, Marc
    Tata Institute of Fundamental Research, Mumbai, India.
    Using combinatorial benchmarks to probe the reasoning power of pseudo-boolean solvers2018In: Proceedings of the 21st International Conference on Theory and Applications of Satisfiability Testing, SAT 2018 Held as Part of the Federated Logic Conference, FloC 2018, Springer, 2018, Vol. 10929, p. 75-93Conference paper (Refereed)
    Abstract [en]

    We study cdcl-cuttingplanes, Open-WBO, and Sat4j, three successful solvers from the Pseudo-Boolean Competition 2016, and evaluate them by performing experiments on crafted benchmarks designed to be trivial for the cutting planes (CP) proof system underlying pseudo-Boolean (PB) proof search but yet potentially tricky for PB solvers. Our experiments demonstrate severe shortcomings in state-of-the-art PB solving techniques. Although our benchmarks have linear-size tree-like CP proofs, and are thus extremely easy in theory, the solvers often perform quite badly even for very small instances. We believe this shows that solvers need to employ stronger rules of cutting planes reasoning. Even some instances that lack not only Boolean but also real-valued solutions are very hard in practice, which indicates that PB solvers need to get better not only at Boolean reasoning but also at linear programming. Taken together, our results point to several crucial challenges to be overcome in the quest for more efficient pseudo-Boolean solvers, and we expect that a further study of our benchmarks could shed more light on the potential and limitations of current state-of-the-art PB solving.

  • 4.
    Giráldez-Cru, Jesús
    et al.
    KTH.
    Lee, J. H. M.
    Meseguer, P.
    Iterative AWC for distributed SAT2017In: 20th International Conference of the Catalan Association for Artificial Intelligence, CCIA 2017, IOS Press , 2017, p. 56-65Conference paper (Refereed)
    Abstract [en]

    Traversing large search spaces can be done more efficiently by exploiting the dead-ends –in formal terms nogoods– discovered during search. If a previously found nogood appears again, the search process can avoid it, saving some search effort. Storing all found nogoods may require exponential memory, which is unaffordable. However, current memories allow to store a large set of nogoods, to be maintained during the solving process. In many cases, a solution is found before memory is exhausted. In the context of Distributed Constraint Satisfaction, the AWC algorithm allows to compute a solution quickly but, to guarantee completeness, it requires storing all found nogoods. Trading space per time, we develop a new iterative version of the algorithm that delays the exponential effects. We present this new version in the context of distributed SAT, where agents hold several Boolean variables. Taking advantage of existing SAT technology, this version perform calls to external MaxSAT solver. Experimentally, we confirm the benefits of the proposed approach on several benchmarks.

  • 5.
    Vinyals, Marc
    et al.
    Inst Fundamental Res, Mumbai, Maharashtra, India.
    Elffers, Jan
    KTH, School of Electrical Engineering and Computer Science (EECS), Theoretical Computer Science, TCS.
    Giráldez-Cru, Jakob
    KTH, School of Electrical Engineering and Computer Science (EECS), Theoretical Computer Science, TCS.
    Gocht, Stephan
    KTH, School of Electrical Engineering and Computer Science (EECS), Theoretical Computer Science, TCS.
    Nordström, Jakob
    KTH, School of Electrical Engineering and Computer Science (EECS), Theoretical Computer Science, TCS.
    In between resolution and cutting planes: A study of proof systems for pseudo-boolean SAT solving2018In: Proceedings of the 21st International Conference on Theory and Applications of Satisfiability Testing, SAT 2018 Held as Part of the Federated Logic Conference, FloC 2018, Springer, 2018, Vol. 10929, p. 292-310Conference paper (Refereed)
    Abstract [en]

    We initiate a proof complexity theoretic study of subsystems of cutting planes (CP) modelling proof search in conflict-driven pseudo-Boolean (PB) solvers. These algorithms combine restrictions such as that addition of constraints should always cancel a variable and/or that so-called saturation is used instead of division. It is known that on CNF inputs cutting planes with cancelling addition and saturation is essentially just resolution. We show that even if general addition is allowed, this proof system is still polynomially simulated by resolution with respect to proof size as long as coefficients are polynomially bounded. As a further way of delineating the proof power of subsystems of CP, we propose to study a number of easy (but tricky) instances of problems in NP. Most of the formulas we consider have short and simple tree-like proofs in general CP, but the restricted subsystems seem to reveal a much more varied landscape. Although we are not able to formally establish separations between different subsystems of CP—which would require major technical breakthroughs in proof complexity—these formulas appear to be good candidates for obtaining such separations. We believe that a closer study of these benchmarks is a promising approach for shedding more light on the reasoning power of pseudo-Boolean solvers.

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