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Jan Elffers

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9 papers
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9

AAAI Conference 2020 Conference Paper

A Cardinal Improvement to Pseudo-Boolean Solving

  • Jan Elffers
  • Jakob Nordstr”m

Pseudo-Boolean solvers hold out the theoretical potential of exponential improvements over conflict-driven clause learning (CDCL) SAT solvers, but in practice perform very poorly if the input is given in the standard conjunctive normal form (CNF) format. We present a technique to remedy this problem by recovering cardinality constraints from CNF on the fly during search. This is done by collecting potential building blocks of cardinality constraints during propagation and combining these blocks during conflict analysis. Our implementation has a non-negligible but manageable overhead when detection is not successful, and yields significant gains for some SAT competition and crafted benchmarks for which pseudo- Boolean reasoning is stronger than CDCL. It also boosts performance for some native pseudo-Boolean formulas where this approach helps to improve learned constraints.

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AAAI Conference 2020 Conference Paper

Justifying All Differences Using Pseudo-Boolean Reasoning

  • Jan Elffers
  • Stephan Gocht
  • Ciaran McCreesh
  • Jakob Nordstr”öm

Constraint programming solvers support rich global constraints and propagators, which make them both powerful and hard to debug. In the Boolean satisfiability community, prooflogging is the standard solution for generating trustworthy outputs, and this has become key to the social acceptability of computer-generated proofs. However, reusing this technology for constraint programming requires either much weaker propagation, or an impractical blowup in proof length. This paper demonstrates that simple, clean, and efficient proof logging is still possible for the all-different constraint, through pseudo-Boolean reasoning. We explain how such proofs can be expressed and verified mechanistically, describe an implementation, and discuss the broader implications for proof logging in constraint programming.

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SAT Conference 2020 Conference Paper

Simplified and Improved Separations Between Regular and General Resolution by Lifting

  • Marc Vinyals
  • Jan Elffers
  • Jan Johannsen
  • Jakob Nordström

Abstract We give a significantly simplified proof of the exponential separation between regular and general resolution of Alekhnovich et al. (2007) as a consequence of a general theorem lifting proof depth to regular proof length in resolution. This simpler proof then allows us to strengthen the separation further, and to construct families of theoretically very easy benchmarks that are surprisingly hard for SAT solvers in practice.

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IJCAI Conference 2018 Conference Paper

Divide and Conquer: Towards Faster Pseudo-Boolean Solving

  • Jan Elffers
  • Jakob Nordström

The last 20 years have seen dramatic improvements in the performance of algorithms for Boolean satisfiability---so-called SAT solvers---and today conflict-driven clause learning (CDCL) solvers are routinely used in a wide range of application areas. One serious short-coming of CDCL, however, is that the underlying method of reasoning is quite weak. A tantalizing solution is to instead use stronger pseudo-Boolean (PB) reasoning, but so far the promise of exponential gains in performance has failed to materialize---the increased theoretical strength seems hard to harness algorithmically, and in many applications CDCL-based methods are still superior. We propose a modified approach to pseudo-Boolean solving based on division instead of the saturation rule used in [Chai and Kuehlmann '05] and other PB solvers. In addition to resulting in a stronger conflict analysis, this also improves performance by keeping integer coefficient sizes down, and yields a very competitive solver as shown by the results in the Pseudo-Boolean Competitions 2015 and 2016.

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SAT Conference 2018 Conference Paper

In Between Resolution and Cutting Planes: A Study of Proof Systems for Pseudo-Boolean SAT Solving

  • Marc Vinyals
  • Jan Elffers
  • Jesús Giráldez-Cru
  • Stephan Gocht
  • Jakob Nordström

Abstract 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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IJCAI Conference 2018 Conference Paper

Seeking Practical CDCL Insights from Theoretical SAT Benchmarks

  • Jan Elffers
  • Jesús Giráldez-Cru
  • Stephan Gocht
  • Jakob Nordström
  • Laurent Simon

Over the last decades Boolean satisfiability (SAT) solvers based on conflict-driven clause learning (CDCL) have developed to the point where they can handle formulas with millions of variables. Yet a deeper understanding of how these solvers can be so successful has remained elusive. In this work we shed light on CDCL performance by using theoretical benchmarks, which have the attractive features of being a) scalable, b) extremal with respect to different proof search parameters, and c) theoretically easy in the sense of having short proofs in the resolution proof system underlying CDCL. This allows for a systematic study of solver heuristics and how efficiently they search for proofs. We report results from extensive experiments on a wide range of benchmarks. Our findings include several examples where theory predicts and explains CDCL behaviour, but also raise a number of intriguing questions for further study.

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SAT Conference 2018 Conference Paper

Using Combinatorial Benchmarks to Probe the Reasoning Power of Pseudo-Boolean Solvers

  • Jan Elffers
  • Jesús Giráldez-Cru
  • Jakob Nordström
  • Marc Vinyals

Abstract 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.

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SAT Conference 2017 Conference Paper

CNFgen: A Generator of Crafted Benchmarks

  • Massimo Lauria
  • Jan Elffers
  • Jakob Nordström
  • Marc Vinyals

Abstract We present CNFgen, a generator of combinatorial benchmarks in DIMACS and OPB format. The proof complexity literature is a rich source not only of hard instances but also of instances that are theoretically easy but “extremal” in different ways, and therefore of potential interest in the context of SAT solving. Since most of these formulas appear not to be very well known in the SAT community, however, we propose CNFgen as a resource to make them readily available for solver development and evaluation. Many formulas studied in proof complexity are based on graphs, and CNFgen is also able to generate, parse and do basic manipulation of such objects. Furthermore, it includes a library cnfformula giving access to the functionality of CNFgen to Python programs.

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SAT Conference 2016 Conference Paper

Trade-offs Between Time and Memory in a Tighter Model of CDCL SAT Solvers

  • Jan Elffers
  • Jan Johannsen
  • Massimo Lauria
  • Thomas Magnard
  • Jakob Nordström
  • Marc Vinyals

Abstract A long line of research has studied the power of conflict-driven clause learning (CDCL) and how it compares to the resolution proof system in which it searches for proofs. It has been shown that CDCL can polynomially simulate resolution even with an adversarially chosen learning scheme as long as it is asserting. However, the simulation only works under the assumption that no learned clauses are ever forgotten, and the polynomial blow-up is significant. Moreover, the simulation requires very frequent restarts, whereas the power of CDCL with less frequent or entirely without restarts remains poorly understood. With a view towards obtaining results with tighter relations between CDCL and resolution, we introduce a more fine-grained model of CDCL that captures not only time but also memory usage and number of restarts. We show how previously established strong size-space trade-offs for resolution can be transformed into equally strong trade-offs between time and memory usage for CDCL, where the upper bounds hold for CDCL without any restarts using the standard 1UIP clause learning scheme, and the (in some cases tightly matching) lower bounds hold for arbitrarily frequent restarts and arbitrary clause learning schemes.

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