Efficient satisfiability solver

The past few decades saw great improvements in the performance of satisfiability (SAT) solvers. In this thesis, we discuss the state-of-the-art techniques used in building an efficient SAT solver. Modern SAT solvers are mainly constituted by the following components: decision heuristics, Boolean constraint propagation, conflict analysis, restart, clause deletion and preprocessing. Various algorithms and implementations in each component will be discussed and analyzed. Then we propose a new backtracking strategy, partial backtracking, which can be easily implemented in SAT solvers. It is essentially an extension of the backtracking strategy used in most SAT solvers. With partial backtracking, the solver consecutively amends the variable assignments instead of discarding them completely so that it does not backtrack as many levels as the classic strategy does after analyzing a conflict. We implemented this strategy in our solver Nigma and the experiments show that the solver benefits from this adjustment

On primal-dual schema for the minimum satisfiability problem

Satisfiability problem is the first problem known to be NP-complete [8, 28]. In this thesis, we have studied the minimization version of the satisfiability problem called the MINSAT. Given a set of boolean variables and a set of clauses, such that each clause is a disjunction of variables, the goal is to find the boolean values of the variables so that minimum number of clauses are satisfied. We have used the concept of linear programming and the primal-dual method to study the problem. We have constructed the Linear program of the MINSAT and its restricted version. We have proposed two combinatorial methods to solve the dual of the restricted primal of the MINSAT. Further to this, these two algorithms also obtain an integral solution to the dual of the MINSAT problem. Lastly, we performed a comparison analysis of our proposed algorithms with the simplex method

Witness generation in existential CTL model checking

Hardware and software systems are widely used in applications where failure is prohibitively costly or even unacceptable. The main obstacle to make such systems more reliable and capable of more complex and sensitive tasks is our limited ability to design and implement them with sufficiently high degree of confidence in their correctness under all circumstances. As an automated technique that verifies the system early in the design phase, model checking explores the state space of the system exhaustively and rigorously to determine if the system satisfies the specifications and detect fatal errors that may be missed by simulation and testing. One essential advantage of model checking is the capability to generate witnesses and counterexamples. They are simple and straightforward forms to prove an existential specification or falsify a universal specification. Beside enhancing the credibility of the model checker\u27s conclusion, they either strengthen engineers\u27 confidence in the system or provide hints to reveal potential defects. In this dissertation, we focus on symbolic model checking with specifications expressed in computation tree logic (CTL), which describes branching-time behaviors of the system, and investigate the witness generation techniques for the existential fragment of CTL, i.e., ECTL, covering both decision-diagram-based and SAT-based. Since witnesses provide important debugging information and may be inspected by engineers, smaller ones are always preferable to ease their interpretation and understanding. To the best of our knowledge, no existing witness generation technique guarantees the minimality for a general ECTL formula with nested existential CTL operators. One contribution of this dissertation is to fill this gap with the minimality guarantee. With the help of the saturation algorithm, our approach computes the minimum witness size for the given ECTL formula in every state, stored as an additive edge-valued multiway decision diagrams (EV+MDD), a variant of the well-known binary decision diagram (BDD), and then builds a minimum witness. Though computationally intensive, this has promising applications in reducing engineers\u27 workload. SAT-based model checking, in particular, bounded model checking, reduces a model checking problem problem into a satisfiability problem and leverages a SAT solver to solve it. Another contribution of this dissertation is to improve the translation of bounded semantics of ECTL into propositional formulas. By realizing the possibility of path reuse, i.e., a state may build its own witness by reusing its successor\u27s, we may generate a significantly smaller formula, which is often easier for a SAT solver to answer, and thus boost the performance of bounded model checking

URSA: A System for Uniform Reduction to SAT

There are a huge number of problems, from various areas, being solved by reducing them to SAT. However, for many applications, translation into SAT is performed by specialized, problem-specific tools. In this paper we describe a new system for uniform solving of a wide class of problems by reducing them to SAT. The system uses a new specification language URSA that combines imperative and declarative programming paradigms. The reduction to SAT is defined precisely by the semantics of the specification language. The domain of the approach is wide (e.g., many NP-complete problems can be simply specified and then solved by the system) and there are problems easily solvable by the proposed system, while they can be hardly solved by using other programming languages or constraint programming systems. So, the system can be seen not only as a tool for solving problems by reducing them to SAT, but also as a general-purpose constraint solving system (for finite domains). In this paper, we also describe an open-source implementation of the described approach. The performed experiments suggest that the system is competitive to state-of-the-art related modelling systems.Comment: 39 pages, uses tikz.st