Abstract. The formulation of a Propositional Satisfiability (SAT) problem instance is vital to efficient solving. This has motivated research on preprocessing, and inprocessing techniques where reformulation of a SAT instance is interleaved with solving. Preprocessing and inprocessing are highly effective in extending the reach of SAT solvers, however they necessarily operate on the lowest leve...

Signed conjunctive normal form (signed CNF) is a classical conjunctive clause form using a generalised notion of literal, called signed literal. A signed literal is an expression of the form S : p, where p is a classical atom and S, its sign, is a subset of a domain N . The informal meaning is “p takes one of the values in S”. Signed formulas are a logical language for knowledge representation ...

FPGA detailed routing problem is an interesting problem in VLSI field because of the limited routing resources in island style FPGA architectures. In this paper, the effectiveness of various switch boxes (Subset, Wilton and Universal) in FPGA detailed routing has been tested using a Boolean satisfiability (SAT) based approach. A SAT instance is formulated for each routing problem and routabilit...

The combinatorial optimization problems are difficult to set up within a parallel context: a search-space is built during the computation and is explored in an irregular way. Moreover, the size of the search-space grows exponentially according to the size of the problem. Since the current processor industry is multiplying the number of cores in their product instead of increasing their frequenc...

This paper solves a long standing open problem of whether NP-complete problems could be solved in polynomial time on a deterministic Turing machine by showing that the indistinguishable binomial decision tree can be formed in a 3-SAT instance. This paper describes how to construct the decision tree and explains why 3-SAT has no polynomial-time algorithm when the decision tree is formed in the 3...

Two widely used problems are the Satisfiability problem (SAT) and the Curriculum-Based Course Timetabling (CB-CTT) problem. The SAT problem searches for an assignment that make true a certain boolean formula. On the other side, the CB-CTT involves the task of scheduling lectures of courses to rooms, considering teacher availability, a specified curricula, and a set of constraints. Given the adv...

Boolean satisfiability (SAT) as a canonical NP-complete decision problem is one of the most important problems in computer science. In practice, real-world SAT sentences are drawn from a distribution that may result in efficient algorithms for their solution. Such SAT instances are likely to have shared characteristics and substructures. This work approaches the exploration of a family of SAT s...

Boolean Satisfiability (SAT) solving has dramatically evolved in the past decade and a half. The outcome, today, is manifested in dozens of high performance and relatively scalable SAT solvers. The significant success of SAT solving technology, specially on practical problem instances, is credited to the aggregation of different SAT enhancements. In this paper, we revisit the organization of mo...

Many practically important combinatorial problems can be efficiently reduced to a problem of Boolean satisfiability (SAT). Therefore, the implementation of distributed algorithms for solving SAT problems is of great importance. In this article we describe a technology for organizing desktop grid, which is meant for solving SAT problems. This technology was implemented in the form of a volunteer...