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It involves determining whether there exists an assignment of boolean values to variables in a given boolean formula, such that the formula evaluates to true. The SAT problem is a well-studied topic, with applications in various fields, including artificial intelligence, circuit design, and software verification. The Wikipedia page on the Boolean satisfiability problem provides a detailed overview of the problem, its history, and its significance. It explains the concept of boolean formulas and illustrates different types of clauses and literals used in SAT. The page also discusses the complexity of the problem and its classification as NP-complete, which means that there is no known efficient algorithm to solve it in the worst case. Additionally, the article covers various techniques and algorithms devised to solve the SAT problem, such as backtracking, local search, and Davis–Putnam–Logemann–Loveland (DPLL) algorithm. It discusses the strengths and weaknesses of these approaches and provides examples and pseudocode to help readers understand their implementation. The Wikipedia page also explores the applications of SAT in solving real-world problems, such as planning, scheduling, and hardware and software verification. It explains how SAT solvers have been used to solve complex industrial design problems and showcases some successful applications in the field. Moreover, the article highlights the challenges faced in solving large-scale instances of SAT and the ongoing research in the field to address these issues. Overall, the Wikipedia page on the Boolean satisfiability problem serves as a comprehensive and informative resource for anyone interested in understanding the theory, algorithms, and applications of SAT.