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Analyse de la complexité des programmes par interprétation sémantique

Romain Pechoux 1
1 CARTE - Theoretical adverse computations, and safety
Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
Abstract : There are several approaches developed by the Implicit Computational Complexity (ICC) community which try to analyze and control program resources. In this document, we focus our study on the resource control with the help of semantics interpretations.
After introducing the notion of quasi-interpretation together with its distinct properties and characterizations, we show the results obtained in the study of such a tool: We study the synthesis problem which consists in finding a quasi-interpretation for a given program and we tackle the issue of quasi-interpretation modularity. Modularity allows to decrease the complexity of the synthesis procedure and to capture more algorithms. We present several extensions of quasi-interpretations to reactive programming, bytecode verification or higher-order programming. Afterwards, we introduce the notion of sup-interpretation. This notion strictly generalizes the one of quasi-interpretation and is used in distinct criteria in order to control the resources of more algorithms, including algorithms over infinite data and algorithms using a divide and conquer strategy. We combine sup-interpretations with distinct termination criteria, such as RPO orderings, dependency pairs or size-change principle, and we compare them to the notion of quasi-interpretation. Using the notion of sup-interpretation, we characterize small parallel complexity classes. We provide some heuristics for the sup-interpretation synthesis: we manage to synthesize sup-interpretations without the subterm property, that is, sup-interpretations which are not quasi-interpretations. Finally, we extend sup-interpretations to object-oriented programs, thus obtaining distinct criteria for resource control of object-oriented programs and their methods.
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https://tel.archives-ouvertes.fr/tel-01752904
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Submitted on : Tuesday, September 16, 2008 - 10:55:37 AM
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  • HAL Id : tel-01752904, version 2

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Romain Pechoux. Analyse de la complexité des programmes par interprétation sémantique. Informatique [cs]. Institut National Polytechnique de Lorraine - INPL, 2007. Français. ⟨NNT : 2007INPL084N⟩. ⟨tel-01752904v2⟩

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