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The so-called synthesis problem for nets, which consists in deciding whether a given graph is isomorphic to the case graph of some net, and then constructing the net, has been solved in the litterature for various types of nets, ranging from elementary nets to Petri nets. The common principle for the synthesis is the idea of regions in graphs, representing possible extensions of places in nets. However, no practical algorithm has been defined so far for the synthesis. We give here exphcit algorithms solving in polynomial time the synthesis problem for bounded nets from regular languages or from finite automata. * This work was partly supported by the French P.R.c. ModUles et Preuves, by the H.C.M. Network Express, and by the H.C.M. fellowship granted to Luca Bernardinello, on leave from the University of Milan.

Abstract:In the field of computer security, a problem that received little attention so far is the enforcement of confidentiality properties by supervisory control. Given a critical system G that may leak confidential information, the problem consists in designing a controller C, possibly disabling occurrences of a fixed subset of events of G, so that the closed-loop system G/C does not leak confidential information. We consider this problem in the case where G is a finite transition system with set of events Σ and an inquisitive user, called the adversary, observes a subset Σ a of Σ. The confidential information is the fact (when it is true) that the trace of the execution of G on Σ * belongs to a regular set S ⊆ Σ * , called the secret. The secret S is said to be opaque w.r.t. G (resp. G/C) and Σ a if the adversary cannot safely infer this fact from the trace of the execution of G (resp. G/C) on Σ * a . In the converse case, the secret can be disclosed. We present an effective algorithm for computing the most permissive controller C such that S is opaque w.r.t. G/C and Σ a . This algorithm subsumes two earlier algorithms working under the strong assumption that the alphabet Σ a of the adversary and the set of events that the controller can disable are comparable.Key-words: discrete event systems, control, security, confidentiality, opacity, partial observation Contrôle par supervision de l'opacitéRésumé : Dans le domaine de la sécurité informatique, le problème de la synthèse de contrôleurs pour assurer des propriétés de confidentialité a pour l'instantété très peuétudié.Étant donné un système critique G, le problème consisteà calculer automatiquement un contrôleur C de telle manière qu'il n'y ait aucune fuite d'information dans G/C. Nous considérons ce problème dans le cas où G est donné par un système de transitions fini sur un alphabet Σ, et un utilisateur, appelé adversaire, qui observe seulement un sous-ensemble Σ a de Σ. L'information confidentielle est modélisée par un langage régulier S ⊆ Σ * , appelé le secret. Le secret S est dit opaque relativementà G et Σ a si l'adversaire ne peut inférer de manière certaine que l'exécution courante de G appartient au secret en se fondant uniquement sur l'observation faite relativementà Σ a . Nous présentons un algorithme effectif permettant de calculer le contrôleur C le plus permissif tel que S soit opaque relativementà G/C et Σ a . Cet algorithmeétend des résultats précédemmentétablis : il n'est effet plus nécessaire de supposer que l'alphabet de l'adversaire Σ a et l'alphabet desévénements contrôlables sont comparables (au sens de l'inclusion).

International audienceThis book is a comprehensive, systematic survey of the synthesis problem, and of region theory which underlies its solution, covering the related theory, algorithms, and applications. The authors focus on safe Petri nets and place/transition nets (P/T-nets), treating synthesis as an automated process which, given behavioural specifications or partial specifications of a system to be realized, decides whether the specifications are feasible, and then produces a Petri net realizing them exactly, or if this is not possible produces a Petri net realizing an optimal approximation of the specifications.In Part I the authors introduce elementary net synthesis. In Part II they explain variations of elementary net synthesis and the unified theory of net synthesis. The first three chapters of Part III address the linear algebraic structure of regions, synthesis of P/T-nets from finite initialized transition systems, and the synthesis of unbounded P/T-nets. Finally, the last chapter in Part III and the chapters in Part IV cover more advanced topics and applications: P/T-nets with the step firing rule, extracting concurrency from transition systems, process discovery, supervisory control, and the design of speed-independent circuits.Most chapters conclude with exercices, and the book is a valuable reference for both graduate students of computer science and electrical engineering and researchers and engineers in this domain