Abstract
Many search algorithms have been introduced without correctness proofs, or proved only with respect to an informal semantics of the algorithm. We address this problem by taking advantage of the correspondence between programs and proofs. We give a single proof of the correctness of a very general search algorithm, for which we provide Scheme code. It is straightforward to implement service functions to implement algorithms such as Davis-Putnam for satisfiability or forward checking (FC) for constraint satisfaction, and to incorporate conflict-directed backjumping (CBJ) and heuristics for variable and value ordering. By separating the search algorithm from problem features, our work should enable the much speedier implementation of sophisticated search methods such as FC-CBJ in new domains, and we illustrate this by sketching an implementation for the Hamiltonian Circuit problem.
Judith Underwood is supported by EPSRC award GR/L/15685. We thank members of APES, particularly Patrick Prosser and Toby Walsh for their code. We especially thank Mr Denis Magnus for his invaluable contributions to our research.
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Gent, I.P., Underwood, J.L. (1997). The logic of search algorithms: Theory and applications. In: Smolka, G. (eds) Principles and Practice of Constraint Programming-CP97. CP 1997. Lecture Notes in Computer Science, vol 1330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017431
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DOI: https://doi.org/10.1007/BFb0017431
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