Constraint satisfaction deals with developing automated techniques for solving computationally hard problems in a declarative fashion. The main emphasis of this thesis is on constraint satisfaction techniques for the propositional satisfiability problem (SAT). As solving techniques for propositional satisfiability have rapidly progressed during the last 15 years, implementations of decision pro...

We report a polynomial time SAT problem instance, the Blocked SAT problem. A blocked clause set, an instance of the Blocked SAT problem, contains only blocked clauses. A close is blocked (for resolution) if it has a literal on which no resolution is possible in the clause set. We know from work of O. Kullmann that a blocked clause can be added or deleted from a clause set without changing its s...

The QXOR-SAT problem is the quantified version of the satisfiability problem XOR-SAT in which the connective exclusive-or is used instead of the usual or. We study the phase transition associated with random QXOR-SAT instances. We give a description of this phase transition in the case of one alternation of quantifiers, thus performing an advanced practical and theoretical study on the phase tr...

The Satisfiability problem (SAT) is a famous NP-Complete problem, which consists of an assignment of Boolean variables (true or false) and some clauses formed of these variables. A clause is a disjunction of some Boolean literals and can be true if and only if any of them is true. A SAT instance is satisfied if and only if all the clauses are simultaneously true. As a generalization of SAT, the...

A fundamental question in Computer Science is understanding when a specific class of problems go from being computationally easy to hard. Because of its generality and applications, the problem of Boolean Satisfiability (aka SAT) is often used as a vehicle for these studies. A signal result from these studies is that the hardness of SAT problems exhibits a dramatic easy-to-hard phase transition...

The MAX-SAT problem is to find a truth assignment that satisfies the maximum number of clauses in a finite set of logical clauses. In the special case of MAX-XOR-SAT, arising from Linear Cryptanalysis, each clause is a set of literals joined by exclusive-or (xor). Solving MAX-XOR-SAT is useful in finding keys to decrypt intercepted encrypted messages. This report presents and evaluates Xor-Walk...

The construction of exact exponential-time algorithms for NP-complete problems has for some time been a very active research area. Unfortunately, there is a lack of general methods for studying and comparing the time complexity of algorithms for such problems. We propose such a method based on clone theory and demonstrate it on the SAT problem. Schaefer has completely classi ed the complexity o...

Introduced here is a novel application of Satisfiability (SAT) to the set membership problem with specific focus on efficiently testing whether large sets contain a given element. Such tests can be greatly enhanced via the use of filters, probabilistic algorithms that can quickly decide whether or not a given element is in a given set. This article proposes SAT filters (i.e., filters based on S...

Problem Q-ALL SAT demands solving a quantified Boolean formula that involves two propositional formulas in conjunctive normal form (CNF). When the first formula has no clauses and thus is trivial, Q-ALL SAT becomes the standard quantified Boolean formula (QBF) at the second level of the polynomial hierarchy. In general, Q-ALL SAT can be converted to second-level QBF by well-known transformation...

Current methods for solving Boolean satisfiability problem (SAT) are scalable enough to solve discrete nonlinear problems involving hundreds of thousands of variables. However, modern SAT solvers scale poorly with problems involving parity constraints (linear equations modulo 2). Gaussian elimination can be used to solve a system of linear equation effectively but it cannot be applied as such w...