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Efficient implementations of DPLL with the addition of clause learning are the fastest complete Boolean satisfiability solvers and can handle many significant real-world problems, such as verification, planning and design. Despite its importance, little is known of the ultimate strengths and limitations of the technique. This paper presents the first(More)
We obtain matching upper and lower bounds for the amount of time to find the predecessor of a given element among the elements of a fixed compactly stored set. Our algorithms are for the unit-cost word RAM with multiplication and are extended to give dynamic algorithms. The lower bounds are proved for a large class of problems, including both static and(More)
While there has been very substantial progress in practical algorithms for satisfiability, there are many related logical problems where satisfiability alone is not enough. One particularly useful extension to satisfiability is the associated counting problem, #SAT, which requires computing the number of assignments that satisfy the input formula. #SAT’s(More)
In this paper we present our results and experiences of using symbolic model checking to study the specification of an aircraft collision avoidance system. Symbolic model checking has been highly successful when applied to hardware systems. We are interested in the question of whether or not model checking techniques can be applied to large software(More)
In this paper we prove an exponential lower bound on the size of bounded-depth Frege proofs for the pigeonhole principle (PHP). We also obtain an Ω(loglogn)-depth lower bound for any polynomial-sized Frege proof of the pigeonhole principle. Our theorem nearly completes the search for the exact complexity of the PHP, as S. Buss has constructed(More)
We obtain matching upper and lower bounds for the amount of time to find the predecessor of a given element among the elements of a fixed efficiently stored set. Our algorithms are for the unit-cost word-level RAM with multiplication and extend to give optimal dynamic algorithms. The lower bounds are proved in a much stronger communication game model, but(More)
We give simple new lower bounds on the lengths of Resolution proofs for the pigeonhole principle and for randomly generated formulas. For random formulas, our bounds signiicantly extend the range of formula sizes for which non-trivial lower bounds are known. For example, we show that with probability approaching 1, any Resolution refutation of a randomly(More)
We consider several problems related to the use of resolution-based methods for determining whether a given boolean formula in conjunctive normal form is satisfiable. First, building on work of Clegg, Edmonds and Impagliazzo, we give an algorithm for satisfiability that when given an unsatisfiable formula of F finds a resolution proof of F , and the runtime(More)