Automatic complexity analysis

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Abstract

We consider the problem of automating the derivation oftight asymptotic complexity bounds for solving Horn clauses. Clearly,the solving time crucially depends on the “sparseness” of the computed relations. Therefore, our asymptotic runtime analysis is accompanied byan asymptotic sparsity calculus together with an asymptotic sparsity analysis. The technical problem here is that least fixpoint iteration failson asymptotic complexity expressions: the intuitive reason is that O(1)+O(1) = O(1) but O(1) + · · · + O(1) may return any value.

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Nielson, F., Nielson, H. R., & Seidl, H. (2002). Automatic complexity analysis. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2305, pp. 243–261). Springer Verlag. https://doi.org/10.1007/3-540-45927-8_18

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