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

Authors:
David Cachera;Thomas Jensen;Arnaud Jobin;Pascal Sotin
Affiliations:
ENS Cachan (Bretagne),;CNRS,;INRIA,;CNRS/DGA, Rennes, France 35042
Venue:
AMAST 2008 Proceedings of the 12th international conference on Algebraic Methodology and Software Technology
Year:
2008

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Abstract

We present a static analysis technique for modeling and approximating the long-run resource usage of programs. The approach is based on a quantitative semantic framework where programs are represented as linear operators over dioids. We provide abstraction techniques for such linear operators which make it feasible to compute safe over-approximations of the long-run cost of a program. A theorem is proved stating that such abstractions yield correct approximations of the program's long-run cost. These approximations are effectively computed as the eigenvalue of the matrix representation of the abstract semantics. The theoretical developments are illustrated on a concrete example taken from the analysis of the cache behaviour of a simple bytecode language.