Non-Redundant Implicational Base of Many-Valued Context Using SAT

Some attribute implications in an implicational base of a derived context of many-valued context can be inferred from some other attribute implications together with its scales. The scales are interpretation of some values in the many-valued context therefore they are a prior or an existing knowledge. In knowledge discovery, the such attribute implications are redundant and cannot be considered as new knowledge. Therefore the attribute implicational should be eliminated. This paper shows that the redundancy problem exists and formalizes a model to check the redundancy

Preprocessing and Stochastic Local Search in Maximum Satisfiability

Problems which ask to compute an optimal solution to its instances are called optimization problems. The maximum satisfiability (MaxSAT) problem is a well-studied combinatorial optimization problem with many applications in domains such as cancer therapy design, electronic markets, hardware debugging and routing. Many problems, including the aforementioned ones, can be encoded in MaxSAT. Thus MaxSAT serves as a general optimization paradigm and therefore advances in MaxSAT algorithms translate to advances in solving other problems. In this thesis, we analyze the effects of MaxSAT preprocessing, the process of reformulating the input instance prior to solving, on the perceived costs of solutions during search. We show that after preprocessing most MaxSAT solvers may misinterpret the costs of non-optimal solutions. Many MaxSAT algorithms use the found non-optimal solutions in guiding the search for solutions and so the misinterpretation of costs may misguide the search. Towards remedying this issue, we introduce and study the concept of locally minimal solutions. We show that for some of the central preprocessing techniques for MaxSAT, the perceived cost of a locally minimal solution to a preprocessed instance equals the cost of the corresponding reconstructed solution to the original instance. We develop a stochastic local search algorithm for MaxSAT, called LMS-SLS, that is prepended with a preprocessor and that searches over locally minimal solutions. We implement LMS-SLS and analyze the performance of its different components, particularly the effects of preprocessing and computing locally minimal solutions, and also compare LMS-SLS with the state-of-the-art SLS solver SATLike for MaxSAT.

Towards Next Generation Sequential and Parallel SAT Solvers

This thesis focuses on improving the SAT solving technology. The improvements focus on two major subjects: sequential SAT solving and parallel SAT solving. To better understand sequential SAT algorithms, the abstract reduction system Generic CDCL is introduced. With Generic CDCL, the soundness of solving techniques can be modeled. Next, the conflict driven clause learning algorithm is extended with the three techniques local look-ahead, local probing and all UIP learning that allow more global reasoning during search. These techniques improve the performance of the sequential SAT solver Riss. Then, the formula simplification techniques bounded variable addition, covered literal elimination and an advanced cardinality constraint extraction are introduced. By using these techniques, the reasoning of the overall SAT solving tool chain becomes stronger than plain resolution. When using these three techniques in the formula simplification tool Coprocessor before using Riss to solve a formula, the performance can be improved further. Due to the increasing number of cores in CPUs, the scalable parallel SAT solving approach iterative partitioning has been implemented in Pcasso for the multi-core architecture. Related work on parallel SAT solving has been studied to extract main ideas that can improve Pcasso. Besides parallel formula simplification with bounded variable elimination, the major extension is the extended clause sharing level based clause tagging, which builds the basis for conflict driven node killing. The latter allows to better identify unsatisfiable search space partitions. Another improvement is to combine scattering and look-ahead as a superior search space partitioning function. In combination with Coprocessor, the introduced extensions increase the performance of the parallel solver Pcasso. The implemented system turns out to be scalable for the multi-core architecture. Hence iterative partitioning is interesting for future parallel SAT solvers. The implemented solvers participated in international SAT competitions. In 2013 and 2014 Pcasso showed a good performance. Riss in combination with Copro- cessor won several first, second and third prices, including two Kurt-Gödel-Medals. Hence, the introduced algorithms improved modern SAT solving technology

SAT and CP: Parallelisation and Applications

This thesis is considered with the parallelisation of solvers which search for either an arbitrary, or an optimum, solution to a problem stated in some formal way. We discuss the parallelisation of two solvers, and their application in three chapters.In the first chapter, we consider SAT, the decision problem of propositional logic, and algorithms for showing the satisfiability or unsatisfiability of propositional formulas. We sketch some proof-theoretic foundations which are related to the strength of different algorithmic approaches. Furthermore, we discuss details of the implementations of SAT solvers, and show how to improve upon existing sequential solvers. Lastly, we discuss the parallelisation of these solvers with a focus on clause exchange, the communication of intermediate results within a parallel solver. The second chapter is concerned with Contraint Programing (CP) with learning. Contrary to classical Constraint Programming techniques, this incorporates learning mechanisms as they are used in the field of SAT solving. We present results from parallelising CHUFFED, a learning CP solver. As this is both a kind of CP and SAT solver, it is not clear which parallelisation approaches work best here. In the final chapter, we will discuss Sorting networks, which are data oblivious sorting algorithms, i. e., the comparisons they perform do not depend on the input data. Their independence of the input data lends them to parallel implementation. We consider the question how many parallel sorting steps are needed to sort some inputs, and present both lower and upper bounds for several cases