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...

The satis ability problem (SAT) is a fundamental problem in mathematical logic, constraint satisfaction, VLSI engineering, and computing theory. Methods to solve the satis ability problem play an important role in the development of computing theory and systems. In this paper, we give a BDD (Binary Decision Diagrams) SAT solver for practical asynchronous circuit design. The BDD SAT solver consi...

The problem of determining whether a propositional Boolean formula can be true is called the Boolean Satisfiability Problem or SAT. SAT is an important and widely studied problem in computer science. In practice, SAT is a core problem in many applications such as Electronic Design Automation (EDA) and Artificial Intelligence (AI). This thesis investigates various problems in the design and impl...

In this paper we restrict every set splitting problem to the special case in which every set has just three elements. This restricted version is also NP-complete. Then, we introduce a general conversion from any set splitting problem to 3-set splitting. Then we introduce a randomize algorithm, and we use Markov chain model for run time complexity analysis of this algorithm. In the last section ...

Many real-world problems are nowadays encoded into SAT instances and efficiently solved by CDCL SAT solvers. However, some scenarios require distributed problem solving approaches. Privacy is often the main reason. This causes the distributed SAT problem. In this work, we analyze how this problem can be tacked in an efficient way, and present ABTSAT, a new version of the ABT algorithm adapted t...

Sudoku is a very simple and well-known puzzle that has achieved international popularity in the recent past. This paper addresses the problem of encoding Sudoku puzzles into conjunctive normal form (CNF), and subsequently solving them using polynomial-time propositional satisfiability (SAT) inference techniques. We introduce two straightforward SAT encodings for Sudoku: the minimal encoding and...

There are many combinatorial puzzles around the world. Solving these puzzles is an intellectual challenge to human kinds. In computing, one way of solving these combinatorial puzzles is by modeling them as a satisfiablility problem (SAT). The SAT problem is to find given a propositional logic formula an assignment of the variables which makes the formula true. In this project, we use Sudoku, th...

The satissability problem (SAT) is a fundamental problem in mathematical logic, constraint satisfaction , VLSI engineering, and computing theory. Methods to solve the satissability problem play an important role in the development of computing theory and systems. Traditional methods treat the SAT problem as a constrained decision problem. During past research, the number of unsatissable clauses...

In this paper with two equivalent representations of the information contained by a SAT formula, the reason why string generated by succinct SAT formula can be greatly compressed is firstly presented based on Kolmogorov complexity theory. Then what strings can be greatly compressed were classified and discussed. In this way we discovered the SAT problem was composed of a basic problem: distingu...

We present a compiler that translates a problem specification into a propositional satisfiability test (SAT). Problems are specified in a logic-based language, called NP-SPEC, which allows the definition of complex problems in a highly declarative way, and whose expressive power is such as to capture all problems which belong to the complexity class NP. The target SAT instance is solved using a...