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This paper depicts algorithms for solving the decision Boolean SatisfiabilityProblem. An extreme problem is formulated to analyze the complexity ofalgorithms and the complexity for solving it. A novel and easy reformulation asa lottery for an extreme case is presented to determine a stable complexityaround $2^n$. The reformulation point out that the decision BooleanSatisfiability Problem can only be solved in exponential time. This impliesthere is not an efficient algorithm for the NP Class.

Lower bound for the Complexity of the Boolean Satisfiability Problem