Petri Net Synthesis

Abstract

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

Characterisation of the state spaces of marked graph Petri nets

“…Our analysis makes use of the region-theoretical approach for the synthesis problem [1,2,11,12]. In the next definition, the triple (R, B, F) mimics the notion of a Petri net place in terms of an lts.…”

Incremental Process Discovery using Petri Net Synthesis

“…Then N ⊆ N (L), i.e. N is formed from a subset of regions of L. 3 Say that a set R ⊆ N (L) of regions is complete w.r.t. a prefix-closed language L if it witnesses all solvable instances of separation problems, i.e.…”

“…The notion of region introduced by Andrzej Ehrenfeucht and Grzegorz Rozenberg [1,2] is at the origin of numerous studies on the synthesis of Petri nets [3] from specifications given by labelled transitions systems or by languages. Algorithmic solutions for the synthesis of Petri nets using linear algebra techniques 1 [4,5,6] and combinatorial techniques [7,8,9] have been used in the context of process discovery [10,11].…”

Adding A/Sync Places to the Synthesis Procedure for Whole-Place Operations Nets with Localities

“…It will be based on a suitably adapted notion of region of a (step) transition system [17,4,3], as well as their locally maximal execution semantics, a special kind of step firing policy (see [25,14]). Regions were introduced in the seminal paper [17] for the class of Elementary Net Systems (en-systems) with sequential execution semantics.…”

“…After that, the original idea has been developed (see, for example, [27]) and extended in several different directions, including: other Petri net classes (e.g., bounded pt-nets without loops [6], pt-nets [26], Flip-flop nets [29], nets with inhibitor arcs [8,28], and nets with localities [25]); synthesis modules of implemented tool frameworks (e.g., Petrify [12], ProM [31], VipTool [5], Genet [9], and Rbminer [30]); application areas (e.g., asynchronous VLSI circuits [12,9,30] and workflows [31]); other semantical execution models (e.g., step sequences [19,28], (local) maximal concurrency [25], and firing policies [14]); and specification formalisms other than transition systems (e.g., languages [13] and scenarios [5]). More details concerning the importance and long term impact of the region concept can be found in the monograph [3].…”