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E-raamat: Petri Net Synthesis

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This 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 inPart III and the chapters in Part IV cover more advanced topics and applications: P/T-net 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 exercises, and the book is a valuable reference for both graduate students of computer science and electrical engineering and researchers and engineers in this domain.

Arvustused

By reading, studying and perhaps using the book Petri net synthesis as a textbook for a course, one takes an interesting and adventurous journey in the field of relating behavioural and structural descriptions of concurrent systems. Petri net synthesis is the best candidate to be a reference book in this field, and reading it is a great pleasure. book is organized in such a way that it can be used as a textbook for several master courses . (Giovanni Michele Pinna, Mathematical Reviews, January, 2017)

This book provides an impressive in-depth account of a wide range of the results and techniques for Petri net synthesis. It covers both theory and algorithms and provides a good insight into applications. It is valuable for novices as well as for researchers as a rich and reliable reference as well as a source of relevant research problems. (Jörg Desel, zbMATH 1351.68003, 2017)

Part I Elementary Net Synthesis
1 Introduction to Elementary Net Synthesis
15(44)
1.1 An Informal Introduction to Elementary Nets
15(2)
1.2 Elementary Net Systems and Their Firing Rule
17(7)
1.3 Regions and Elementary Transition Systems
24(11)
1.4 Admissible Sets of Regions and the Separation Axioms
35(7)
1.5 Minimal Regions Are Sufficient for Synthesis
42(3)
1.6 Minimal Admissible Sets of Regions
45(3)
1.7 Regions and State Machine Decompositions
48(3)
1.8 Regions of Labelled Partial 2-Structures †
51(8)
Problems
56(2)
Further Reading
58(1)
2 Other Forms of the Synthesis Problem
59(24)
2.1 Canonical Net Versions Yield Optimal Realizations
59(7)
2.2 Relaxing the State Separation Property
66(6)
2.3 Net Synthesis from Languages
72(6)
2.4 Minimal Regions and Approximate Synthesis
78(2)
2.5 Minimal Regions and Synthesis up to Language Equivalence
80(3)
Problems
81(2)
3 Algorithms of Elementary Net Synthesis
83(38)
3.1 NP-Completeness of Synthesis †
83(7)
3.1.1 The Separation Problems Are NP-Complete
84(3)
3.1.2 The Elementary Net Synthesis Problem Is NP-Complete
87(3)
3.2 Algorithms of Elementary Net Synthesis
90(31)
3.2.1 Rough Sets
91(4)
3.2.2 Signatures of Rough Sets
95(3)
3.2.3 Rough Regions
98(3)
3.2.4 Extracting Regions from a Rough Region
101(2)
3.2.5 Net Synthesis Algorithms
103(4)
3.2.6 The Heuristic Approach of Petrify
107(2)
Problems
109(12)
Part II Types of Nets
4 Variations of Elementary Net Synthesis
121(32)
4.1 The Synthesis of Event/Condition Nets
121(8)
4.2 Types of Nets
129(7)
4.3 Regions as Morphisms and Synthesized Nets
136(3)
4.4 Boolean Nets †
139(14)
Problems
147(6)
5 A Unified Theory of Net Synthesis
153(34)
5.1 Duality Between Nets and Transition Systems
155(5)
5.2 Representation Results
160(4)
5.3 Taking Concurrency into Account †
164(23)
5.3.1 Transition Systems with a Concurrency Relation
165(4)
5.3.2 Step Transition Systems
169(8)
Problems
177(4)
Further Reading
181(6)
Part III P/T-Net Synthesis
6 The Linear Algebraic Structure of Regions
187(26)
6.1 Flip-Flop Net Synthesis
187(7)
6.2 Introduction to P/T-Nets and P/T-Regions
194(4)
6.3 Algebraic Structure of P/T-Regions
198(15)
Problems
210(3)
7 Synthesis of P/T-Nets from Finite Initialized Transition Systems
213(14)
7.1 Exact Synthesis of Pure P/T-Nets
213(5)
7.2 Approximate Synthesis of Pure P/T-Nets
218(2)
7.3 Synthesis of Impure P/T-Nets
220(1)
7.4 Synthesis of Bounded Nets from Regular Languages
221(1)
7.5 Synthesis of Pure and Bounded Nets from Finite Languages
222(1)
7.6 Open Issues †
223(4)
Problems
225(2)
8 Synthesis of Unbounded P/T-Nets
227(26)
8.1 Rational Sets and Semilinear Sets
227(3)
8.2 Unbounded P/T-Regions of Languages
230(4)
8.3 Synthesis of Unbounded P/T-Nets from Languages
234(4)
8.4 Unbounded P/T-Regions of Transition Systems †
238(2)
8.5 Synthesis of Nets from Infinite Transition Systems †
240(13)
9 P/T-Nets with the Step Firing Rule †
253(16)
9.1 Regions of Step Transition Systems
254(1)
9.2 P/T-Net Realization of Finite Step Transition Systems
255(4)
9.3 P/T-Net Realization of Step Languages
259(1)
9.4 Partial Languages and Token Flows
260(9)
Part IV Applications of Net Synthesis
10 Extracting Concurrency from Transition Systems †
269(14)
10.1 Distributed Realization of Transition Systems
269(10)
10.1.1 Distributed Transition Systems
270(1)
10.1.2 Distributable P/T-Nets
271(2)
10.1.3 Splitting a Distributable Net into Pieces
273(1)
10.1.4 Distributed Implementation of a Transition System
273(3)
10.1.5 Synthesizing Distributable P/T-Nets
276(3)
10.2 Compacting Automata and Products of Automata
279(4)
11 Process Discovery †
283(18)
11.1 Discovering Workflow Nets from Event Logs
283(4)
11.2 Logs and Their Regions
287(8)
11.3 P/T Net Identification
295(6)
Problems
297(4)
12 Supervisory Control †
301(18)
12.1 Ramadge and Wonham's Theory of Supervisory Control
301(3)
12.2 Petri Net Supervisory Control
304(1)
12.3 Region-Based Supervisory Control of Petri Nets
305(7)
12.4 Region-Based Supervisory Control of Discrete Event Systems
312(3)
12.5 Distributed Control of Discrete Event Systems
315(4)
13 Design of Speed Independent Circuits †
319(18)
References
327(10)
Index 337
Dr. Eric Badouel is a researcher at IRISA/INRIA RennesBretagne Atlantique in Rennes. His research interests include concurrency and Petri nets.

 

Dr. Luca Bernardinello is a researcher in the Dipartimento di Informatica, Sistemistica e Comunicazione of the Università degli studi di Milano-Bicocca. His research interests include concurrency and Petri nets.

 

Dr. Philippe Darondeau was a researcher at IRISA/INRIA RennesBretagne Atlantique in Rennes. His research interests included concurrency and Petri nets. Dr. Darondeau passed away in 2013, during the final writing of the book.