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Long-run cost analysis by approximation of linear operators over dioids

Published online by Cambridge University Press:  03 June 2010

DAVID CACHERA ,
THOMAS JENSEN ,
ARNAUD JOBIN  and
PASCAL SOTIN
DAVID CACHERA
Affiliation:
IRISA/ENS Cachan (Bretagne), Campus de Beaulieu, F-35042 Rennes cedex, France Email: david.cachera@irisa.fr
THOMAS JENSEN
Affiliation:
IRISA/CNRS, Campus de Beaulieu, F-35042 Rennes cedex, France Email: thomas.jensen@irisa.fr
ARNAUD JOBIN
Affiliation:
Université Rennes 1, Campus de Beaulieu, F-35042 Rennes cedex, France Email: arnaud.jobin@irisa.fr
PASCAL SOTIN
Affiliation:
CNRS/DGA, F-35042 Rennes cedex, France Email: pascal.sotin@irisa.fr
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Abstract

In this paper we present a semantics-based framework for analysing the quantitative behaviour of programs with respect to resource usage. We start from an operational semantics in which costs are modelled using a dioid structure. The dioid structure of costs allows the definition of the quantitative semantics as a linear operator. We then develop a theory of approximation of such a semantics, which is akin to what is offered by the theory of abstract interpretation for analysing qualitative properties, in order to compute effectively global cost information from the program. We focus on the notion of long-run cost, which models the asymptotic average cost of a program. The abstraction of the semantics has to take two distinct notions of order into account: the order on costs and the order on states. We prove that our abstraction technique provides a correct approximation of the concrete long-run cost of a program.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 20 , Issue 4 , August 2010 , pp. 589 - 624
Copyright
Copyright © Cambridge University Press 2010

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