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.

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

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