Habilitation à Diriger les Recherches Mention Informatique

Introduction quid est ergo tempus? si nemo ex me quaerat, scio; si quaerenti explicare velim, nescio. What then is time? If no one asks me, I know; if I wish to explain it to one that asketh, I know not. 1 The present document is about time, in at least two respects. Firstly, it gives a description of my scientific work over the time since the completion of my PhD thesis [85]. Secondly, this text tells about efforts to seize and understand the dynamics of asynchronous discrete event systems; that is, how they involve in time, and how this evolution can be detected or predicted if time is not global. The fascination for Petri nets that had led me to the thesis has not faded since then, and will certainly show in the pages the reader is currently holding, or reading on a screen. However, the perspectives have been broadened, if not reversed, since then: while the subject of my thesis had been the characterization of well-structured nets (i.e. such that their structure allows a safe and live marking) by purely relational and topological/graph theoretical means, my work since then has focused on the contrary on the behaviour of given asynchronous systems and how to extract information from it; my work has often not been related to Petri nets at all, see in particular Chapter 6. In the present work, I give an account of efforts and results in this research, structured primarily according to the relations between different subjects (and not the historical order). Of course, many results here have been obtained not in solitary labor but rather in teamwork, as witnessed by the co-author list of the corresponding references. My thanks go to all the colleagues-the friends, in fact-who have accepted to work with me and thus made the present thesis possible. As for the description, it is hoped the central ideas become clear in the respective parts of the description; however, the proofs are almost always omitted here, and the reader who desires to know more is referred to the original works cited. The presentation will start in Chapter 2 from the basic model of Petri nets, and describe the general results obtained; in particular, the chapter tells what blocking a transition can teach about the asymptotic throughput in Free Choice nets, and why this method is of much smaller avail elsewhere. Chapter 2 concludes by introducing …