ABSTRACT. In this paper we present new implementation details and benchmarking results for our parallel portfolio solver \topo. In particular, we discuss ideas and implementation details for the exchange of learned clauses in a massively-parallel SAT solver which is designed to run more that $1,000$ solver threads in parallel. Furthermore, we go back to the roots of portfolio SAT solving, and discuss the impact of diversifying the solver by using different restart- , branching- and clause database management heuristics. We show that these techniques can be used to tune the solver towards different problems. However, in a case study on formulas derived from Bounded Model Checking problems we see the best performance when using a rather simple clause exchange strategy. We show details of these tests and discuss possible explanations for this phenomenon.

As computing times on massively-parallel clusters are expensive, we consider it especially interesting to share these kind of experimental results.

ABSTRACT. Performing hundreds of test runs and a source-code analysis, we empirically identified improved parameter configurations for the CryptoMiniSat (CMS) 5 for solving cryptographic CNF instances originating from algebraic known-plaintext attacks on 3 rounds encryption of the Small AES-64 model cipher. We finally became able to reconstruct 64-bit long keys in under an hour CPU time which, to our knowledge, has never been achieved so far. Especially, not without any assumptions or previous knowledge of key-bits (for instance in the form of side-channels, as in~\cite{Mohamed2012algebraicSCA}). A statistical analysis of the non-deterministic solver runtimes was carried out and command line parameter combinations were defined to yield best runtimes which ranged from under an hour to a few hours in median at the beginning. We proceeded using an Automatic Algorithm Configuration (AAC) tool to systematically extend the search for even better solver configurations with success to deliver even shorter solving times. In this work we elaborate on the systematics we followed to reach our results in a traceable and reproducible way. The ultimate focus of our investigations is to find out if CMS, when appropriately tuned, is indeed capable to attack even bigger and harder problems than the here solved ones. For the domain of cryptographic research, the duration of the solving time plays an inferior role as compared to the practical feasibility of finding a solution to the problem. The perspective scalability of the here presented results is the object of further investigations.

ABSTRACT. DRAT proofs have become the de facto standard for certifying SAT solvers' results. State-of-the-art DRAT checkers are able to efficiently establish the unsatisfiability of a formula. However, DRAT checking requires unit propagation, and so it is computationally non-trivial. Due to design decisions in the development of early DRAT checkers, the class of proofs accepted by state-of-the-art DRAT checkers differs from the class of proofs accepted by the original definition. In this paper, we formalize the operational definition of DRAT proofs, and discuss practical implications of this difference for generating as well as checking DRAT proofs. We also show that these theoretical differences have the potential to affect whether some proofs generated in practice by SAT solvers are correct or not.

ABSTRACT. A Pseudo-Boolean (PB) constraint is a linear inequality constraint over Boolean variables. A popular idea to solve PB-constraints is to transform them to CNFs (via BDDs, adders and sorting networks) and process them using -- increasingly improving -- state-of-the-art SAT-solvers. Recent research have favored the approach that use Binary Decision Diagrams (BDDs), which is evidenced by several new constructions and optimizations. We show that encodings based on comparator networks can still be very competitive. We present a system description of a PB-solver based on MiniSat+ which we extended by adding a new construction of a selection network called 4-Way Merge Selection Network, with a few optimizations based on other solvers. Experiments show that on many instances of popular benchmarks our technique outperforms other state-of-the-art PB-solvers.

ABSTRACT. Experimental data and benchmarks play a crucial role in developing new algorithms and implementations of SAT solvers. Besides comparing and evaluating solvers, they provide the basis for all kinds of experiments, for setting up hypothesis and for testing them. Currently -- even though some initiatives for setting up benchmark databases have been undertaken, and the SAT Competitions provide a ``standardized'' collection of instances -- it is hard to assemble benchmark sets with prescribed properties. Moreover, the origin of SAT instances is often not clear, and benchmark collections might contain duplicates. In this paper we suggest a framework to store meta-data information about SAT instances and provide a framework for collecting, assessing and distributing benchmark metadata.

ABSTRACT. It has been an ongoing debate for a long time about how SAT solvers and in general different or new algorithms should be evaluated and compared both in competitions and more importantly in papers. Evaluations are usually performed on existing benchmarks. Cross-validation and other means to avoid over-fitting are rarely used. In this paper we revisit the old idea of scrambling benchmarks also used in early competitions. Scrambling has the goal to make results of such evaluations more robust. We present a new method for scrambling CNFs, which allows to gradually increase the effect of scrambling, from keeping the scrambled CNF close to the original CNF, to complete random permutation of variables, clauses, and phases of literals. We used this method to scramble benchmarks from the last two SAT competitions and solved them with the best solvers in the main track of the last SAT competition. As expected our experimental results suggest that scrambling has a substantial effect on the performance of individual solvers but surprisingly has little effect on rankings among solvers. As a consequence we argue that only using our method of scrambling is not enough to increase robustness of competitions and evaluations in general.