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The goal of this dissertation is to develop computational tools for solving hard search problems. We focus on a declarative approach in which we write programs to capture constraints of search problems rather than the step-by-step algorithms that solve the search problems. Once we write the declarative program that captures a search problem, we want to compute the solutions of the search problem as well. We realize this goal by applying specially designed software called solvers on the declarative program we have written. Efficient algorithms and implementations of the solvers make the declarative approach practical in solving hard search problems. In the dissertation, we investigate one such declarative programming formalism called logic programming with stable model semantics. In this formalism, a program is a collection of rules. Rules are built of monotone (or convex) abstract constraint atoms. This formalism extends the normal logic programming with stable model semantics, which has been studied by the community for decades and has rich theories and practical applications. We show in the thesis that the stable model semantics and properties, especially those that are concerned with computation of stable models, extend to logic programs with monotone (or convex) abstract constraint atoms. Lparse programming, a version of logic programming with stable model semantics, was proposed in 1990's and has been shown to be an effective programming formalism for solving search problems. Lparse-programs also extends normal logic programs with specific constraint atoms: pseudoboolean constraints. We show in the thesis that pseudoboolean constraints are convex. Thus the theoretical results we obtain for logic programs with convex abstract constraint atoms instantiate to Lparse-programs. Based on these results, we design a solver that computes stable models of lparse-programs via pseudoboolean solvers. We also study the propositional logic extended with pseudoboolean constraints, a byproduct of our research on lparse-programs. We designed and implemented a family local search solvers that compute models of theories in this logic. We performed experimental study on the solvers we developed. The results show that our solvers are efficient in solving many NP-hard search problems.