Synthèse De Travaux Présentés Pour Obtenir Le Diplôme Habilitation À Diriger Les

study of implicit complexity criteria. In the paper [BDLM06] with Dal Lago (Bologna) and Moyen (LIPN), we have started to analyze the behaviour of programs (first-order term rewriting systems) satisfying the implicit complexity criterion for the characterization of Ptime from [BMM07] (that we call here the P-criterion), based on quasi-interpretations. For that we have used a notion of abstraction on programs, called blind abstraction. We would like to continue this line of research by studying various ICC criteria and aim at : – for a given criterion, finding out necessary conditions on the behaviour of programs satisfying the criterion, for instance by using various notions of abstractions on programs ; – possibly, for certain criteria giving some necessary and sufficient conditions on the behaviour of the program for it to meet the criterion. There are several motivations for that. First this approach could help in understanding the theoretical limitations of these implicit complexity criteria, and allow for instance to state a priori that certain families of programs will not be characterizable by a given criterion. On the other hand this could also be a way to compare together different ICC criteria, by comparing the respective classes of programs that they each allow to delineate. Finally from a pragmatic viewpoint, we can use these characterizations in order to obtain ideas on how to extend or generalize the initial criterion considered. This is for instance what we have done already in the case of the P-criterion [BDLM06], by generalizing the notion of recursive path ordering (RPO) that is used in the P-criterion and proving that the complexity property remains valid with this weaker assumption. Another interesting direction in the general study of ICC criteria deals with the difficulty of the associated decision problems. Recall that the general problem, given a program, to decide if it is