The research community on complex networks has developed techniques of analysis and algorithms that can be used by the SAT community to improve our knowledge about the structure of industrial SAT instances. It is often argued that modern SAT solvers are able to exploit this hidden structure, without a precise definition of this notion. In this paper, we show that most industrial SAT instances h...

We describe LMHS, an open source weighted partial maximum satisfiability (MaxSAT) solver. LMHS is a hybrid SAT-IP MaxSAT solver that implements the implicit hitting set approach to MaxSAT. On top of the main algorithm, LMHS offers integrated preprocessing, solution enumeration, an incremental API, and the use of a choice of SAT and IP solvers. We describe the main features of LMHS, and give emp...

The parameterized satisfiability problem over a set of Boolean relations Γ (SAT(Γ)) is the problem of determining whether a conjunctive formula over Γ has at least one model. Due to Schaefer’s dichotomy theorem the computational complexity of SAT(Γ), modulo polynomial-time reductions, has been completely determined: SAT(Γ) is always either tractable or NP-complete. More recently, the problem of...

Bankrechtliche Meldepflichten sind nicht erst seit der Finanzkrise ein relevantes Forschungsfeld. Jedoch werden insbesondere Methoden zur Unterstützung eines rechtsund regelkonformen Berichtswesens derzeit in der Forschung unzureichend betrachtet. Mit der Entwicklung einer Methode zur Modellierung und Analyse von Berichtsregulierungen mit dem Fokus auf den Finanzsektor wird ein Weg aufgezeigt, ...

A graph G is said to be F-saturated if G does not contain a copy of F as a subgraph and G+ e contains a copy of F as a subgraph for any edge e contained in the complement of G. Erdős et al. in [A problem in graph theory, Amer. Math. Monthly 71 (1964) 1107–1110.] determined the minimum number of edges, sat(n, F ), such that a graph G on n vertices must have when F is a t-clique. Later, Ollmann [...

background and objective: magnetic resonance imaging (mri) is the most sensitive technique to detect multiple sclerosis (ms) plaques in central nervous system. in some cases, the patients who were suspected to ms, whereas mri images are normal, but whether patients don’t have ms plaques or mri images are not enough optimized enough in order to show ms plaques? the aim of the current study is ev...

Fix a set S ⊆ {0, 1}∗ of exponential size, e.g. |S ∩ {0, 1}n| ∈ Ω(αn), α > 1. The S-SAT problem asks whether a propositional formula F over variables v1, . . . , vn has a satisfying assignment (v1, . . . , vn) ∈ {0, 1}n ∩S. Our interest is in determining the complexity of S-SAT. We prove that S-SAT is NP-complete for all context-free sets S. Furthermore, we show that if S-SAT is in P for some e...

A graph G is called F -saturated if it does not contain any copy of F , but for any edge e in the complement of G the graph G + e contains some F . The minimum size of an n-vertex F -saturated graph is denoted by sat(n, F ). We give almost exact asymptotics for sat(n,Ck) as k is fixed and n → ∞ where Ck is a cycle with length k.

Propositional model counting or #SAT is the problem of computing the number of models for a given propositional formula, i.e., the number of distinct truth assignments to variables for which the formula evaluates to true. For a proposi-tional formula F , we will use #F to denote the model count of F. This problem is also referred to as the solution counting problem for SAT. It generalizes SAT a...