Norbert Manthey

Automated reencoding of boolean formulas

We present a novel preprocessing technique to automatically reduce the size of Boolean formulas. This technique, called Bounded Variable Addition (BVA), exchanges clauses for variables. Similar to other preprocessing techniques, BVA greedily lowers the sum of variables and clauses, a rough measure for the hardness to solve a formula. We show that cardinality constraints (CCs) can efficiently be reencoded: from a naive CC encoding, BVA automatically generates a compact encoding, which is smaller than sophisticated encodings. Experimental results show that applying BVA can improve SAT solving performance.

Coprocessor 2.0: a flexible CNF simplifier

This paper presents the CNF simplifier Coprocessor 2.0, an extension of Coprocessor [1]. It implements almost all currently known simplification techniques in a modular way and provides access to each single technique to execute them independently. Disabling preprocessing for a set of variables is also possible and enables to apply simplifications also for incremental SAT solving. Experiments show that Coprocessor 2.0 performs better than its predecessor or SatElite[2].

Solving periodic event scheduling problems with SAT

In this paper, periodic event scheduling problems (PESP) are encoded as satisfiability problems (SAT) and solved by a state-of-the-art SAT solver. Two encodings, based on direct and order encoded domains, are presented. An experimental evaluation suggests that the SAT-based approach using order encoding outperforms constraint-based PESP solvers, which until now were considered to be the best solvers for PESP. This opens the possibility to model significantly larger real-world problems.

SAT-Based analysis and quantification of information flow in programs

Quantitative information flow analysis (QIF) is a portfolio of security techniques quantifying the flow of confidential information to public ports. In this paper, we advance the state of the art in QIF for imperative programs. We present both an abstract formulation of the analysis in terms of verification condition generation, logical projection and model counting, and an efficient concrete implementation targeting ANSI C programs. The implementation combines various novel and existing SAT-based tools for bounded model checking, #SAT solving in presence of projection, and SAT preprocessing. We evaluate the technique on synthetic and semi-realistic benchmarks.

Detecting Cardinality Constraints in CNF

We present novel approaches to detect cardinality constraints expressed in CNF. The first approach is based on a syntactic analysis of specific data structures used in SAT solvers to represent binary and ternary clauses, whereas the second approach is based on a semantic analysis by unit propagation. The syntactic approach computes an approximation of the cardinality constraints AtMost-1 and AtMost-2 constraints very fast, whereas the semantic approach has the property to be generic, i.e. it can detect cardinality constraints AtMost-k for any k, at a higher computation cost. Our experimental results suggest that both approaches are efficient at recovering AtMost-1 and AtMost-2 cardinality constraints.

Improving resource-unaware SAT solvers

The paper discusses cache utilization in state-of-the-art SAT solvers. The aim of the study is to show how a resource-unaware SAT solver can be improved by utilizing the cache sensibly. The analysis is performed on a CDCL-based SAT solver using a subset of the industrial SAT Competition 2009 benchmark. For the analysis, the total cycles, the resource stall cycles, the L2 cache hits and the L2 cache misses are traced using sample based profiling. Based on the analysis, several techniques - some of which have not been used in SAT solvers so far - are proposed resulting in a combined speedup up to 83% without affecting the search path of the solver. The average speedup on the benchmark is 60%. The new techniques are also applied to MiniSAT2.0 improving its runtime by 20% on average.

Designing scalable parallel SAT solvers

Solving instances of the propositional satisfiability problem (SAT) in parallel has received a significant amount of attention as the number of cores in a typical workstation is steadily increasing. With the increase of the number of cores, in particular the scalability of such approaches becomes essential for fully harnessing the potential of modern architectures. The best parallel SAT solvers have, until recently, been based on algorithm portfolios, while search-space partitioning approaches have been less successful. We prove, under certain natural assumptions on the partitioning function, that search-space partitioning can always result in an increased expected run time, justifying the success of the portfolio approaches. Furthermore, we give first controlled experiments showing that an approach combining elements from partitioning and portfolios scales better than either of the two approaches and succeeds in solving instances not solved in a recent solver competition.

Soundness of inprocessing in clause sharing SAT solvers

We present a formalism that models the computation of clause sharing portfolio solvers with inprocessing. The soundness of these solvers is not a straightforward property since shared clauses can make a formula unsatisfiable. Therefore, we develop characterizations of simplification techniques and suggest various settings how clause sharing and inprocessing can be combined. Our formalization models most of the recent implemented portfolio systems and we indicate possibilities to improve these. A particular improvement is a novel way to combine clause addition techniques --- like blocked clause addition --- with clause deletion techniques --- like blocked clause elimination or variable elimination.

A compact encoding of pseudo-boolean constraints into SAT

Many different encodings for pseudo-Boolean constraints into the Boolean satisfiability problem have been proposed in the past. In this work we present a novel small sized and simple to implement encoding. The encoding maintains generalized arc consistency by unit propagation and results in a formula in conjunctive normal form that is linear in size with respect to the number of input variables. Experimental data confirms the advantages of the encoding over existing ones for most of the relevant pseudo-Boolean instances.

A More Compact Translation of Pseudo-Boolean Constraints into CNF Such That Generalized Arc Consistency Is Maintained

In this paper we answer the open question for the existence of a more compact encoding from Pseudo-Boolean constraints into CNF that maintains generalized arc consistency by unit propagation, formalized by Bailleux et al. in [21]. In contrast to other encodings our approach is defined in an abstract way and we present a concrete instantiation, resulting in a space complexity of \(\mathcal{O}(n^2 \text{\,log}^2(n)\text{\,log}(w_{\mathsf{max}}))\) clauses in contrast to \(\mathcal{O}(n^3 \text{\,log}(n)\text{\,log}(w_{\mathsf{max}}))\) clauses generated by the previously best known encoding that maintains generalized arc consistency.