Long-Run Cost Analysis by Approximation of Linear Operators over Dioids

David Cachera 1 Thomas Jensen 1 Arnaud Jobin 1 Pascal Sotin 1
1 Lande - Logiciel : ANalyse et DEveloppement
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : We present a static analysis technique for modeling and approxi- mating the long-run resource usage of programs. The approach is based on a quantitative semantic framework where programs are represented as linear op- erators over dioids. We show how to extract the long-run cost of a program from the matrix representation of its semantics. An essential contribution is to provide abstraction techniques which make it feasible to compute safe over- approximations of this cost. A theorem is proved stating that such abstractions yield correct approximations of the program's long-run cost. The theoretical developments are illustrated on a concrete example taken from the analysis of the cache behaviour of a simple bytecode language.
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David Cachera, Thomas Jensen, Arnaud Jobin, Pascal Sotin. Long-Run Cost Analysis by Approximation of Linear Operators over Dioids. [Research Report] RR-6338, INRIA. 2007, pp.35. ⟨inria-00182338v4⟩

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