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Pseudo-Boolean constraints are omnipresent in practical applications, and therefore a significant effort has been devoted to the development of good SAT encoding techniques for these constraints. Some of these encodings first construct a Binary Decision Diagram (BDD) for the constraint, and then encode the BDD into a propositional formula. These BDD-based… (More)
In this paper, we present a new decompositional approach for the extraction of propositional rules from feed-forward neural networks of binary threshold units. After decomposing the network into single units, we show how to extract rules describing a unit’s behavior. This is done using a suitable search tree which allows the pruning of the search space.… (More)
Pseudo-Boolean constraints are omnipresent in practical applications, and thus a significant effort has been devoted to the development of good SAT encoding techniques for them. Some of these encodings first construct a Binary Decision Diagram (BDD) for the constraint, and then encode the BDD into a propositional formula. These BDD-based approaches have… (More)
The management of Urban Wastewater Systems (UWS) requires a comprehensive understanding of the interactions of processes and substances in the system. This leads to complex numerical models which can be applied to predict management actions or understand misconduction of the system. Nevertheless, for the communication between stakeholders in the process of… (More)
Linear constraints are the most common constraints occurring in combinatorial problems. For some problems which combine linear constraints with highly combinatorial constraints, the best solving method is translation to SAT. Translation of a single linear constraint to SAT is a well studied problem, particularly for cardinality and pseudoBoolean… (More)
We compare both pure SAT and hybrid CP/SAT models for solving car sequencing problems, and close 13 out of the 23 large open instances in CSPLib. Three features of these models are crucial to improving the state of the art in this domain. For quickly finding solutions, advanced CP heuristics are important and good propagation (either by a specialized… (More)
Decisions diagrams such as Binary Decision Diagrams (BDDs), Multi-valued Decision Diagrams (MDDs) and Negation Normal Forms (NNFs) provide succinct ways of representing Boolean and other finite functions. Hence they provide a powerful tool for modelling complex constraints in discrete satisfaction and optimization problems. Generic propagators for these… (More)
Boolean Satisfiability (SAT) solvers are a mature technology to solve hard combinatorial problems. The input to a SAT solver is the problem translated to propositional logic in conjunctive normal form (CNF). This thesis studies such translations and aims to make SAT solvers more accessible to non-encoding experts.
Car sequencing is a well known NP-complete problem. This paper introduces encodings of this problem into CNF based on sequential counters. We demonstrate that SAT solvers are powerful in this domain and report new lower bounds for the benchmark set in the CSPLib.
Lazy Clause Generation (LCG) solvers dominate the current constraint programming competitions. These solvers successfully combine systematic propagation based search, global constraints and conflict clause learning from SAT solving into a hybrid approach. My research project extends the LCG methodology by using a mix of eager and lazy encodings and a richer… (More)