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Petri net algebra:

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Bibliographic Details
Main Authors:	Best, Eike 1951- (Author), Devillers, Raymond (Author), Koutny, Maciej (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2001
Series:	Monographs in theoretical computer science
Subjects:	Ciência da computação Informatique - Mathématiques Parallélisme (Informatique) Petri netwerken Redes de petri Álgebra Informatik Mathematik Computer science > Mathematics Parallel processing (Electronic computers) Petri nets Prozessalgebra Petri-Netz
Online Access:	Inhaltsverzeichnis
Physical Description:	XI, 378 S. graph. Darst.
ISBN:	3540673989

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adam_text	EIKE BEST RAYMOND DEVILLERS MACIEJ KOUTNY PETRI NET ALGEBRA WITH 111 FIGURES SPRINGER CONTENTS 1. INTRODUCTION 1 2. THE PETRI BOX CALCULUS 7 2.1 AN INFORMAL INTRODUCTION TO CCS 8 2.2 AN INFORMAL INTRODUCTION TO PETRI NETS 9 2.3 THE STRUCTURE AND BEHAVIOUR OF PBC EXPRESSIONS 11 2.4 SEQUENTIAL COMPOSITION 14 2.5 SYNCHRONISATION 15 2.6 SYNCHRONISATION AND PARALLEL COMPOSITION 21 2.7 OTHER PBC OPERATORS 24 2.8 MODELLING A CONCURRENT PROGRAMMING LANGUAGE 25 2.9 LITERATURE AND BACKGROUND 28 3. SYNTAX AND OPERATIONAL SEMANTICS 29 3.1 STANDARD PBC SYNTAX 29 3.2 STRUCTURED OPERATIONAL SEMANTICS 33 3.2.1 THE BASIC SETUP 35 3.2.2 EQUIVALENCE NOTIONS 37 3.2.3 ELEMENTARY ACTIONS 41 3.2.4 PARALLEL COMPOSITION 42 3.2.5 CHOICE COMPOSITION 45 3.2.6 SEQUENTIAL COMPOSITION 46 3.2.7 SYNCHRONISATION 47 3.2.8 STANDARD PBC SYNCHRONISATION 47 3.2.9 AUTO-SYNCHRONISATION AND MULTILINK-SYNCHRONISATION . . 50 3.2.10 STEP-SYNCHRONISATION 52 3.2.11 BASIC RELABELLING 53 3.2.12 RESTRICTION '. 54 3.2.13 SCOPING 55 3.2.14 ITERATION 58 3.2.15 RECURSION 59 3.3 EXTENSIONS 62 3.3.1 GENERALISED ITERATIONS 62 3.3.2 DATA VARIABLES 64 VIII CONTENTS 3.3.3 GENERALISED CONTROL FLOW OPERATORS 66 3.3.4 GENERALISED COMMUNICATION INTERFACE OPERATORS 67 3.4 EXTENDED PBC SYNTAX 69 3.5 EXAMPLES OF TRANSITION SYSTEMS 69 3.6 LITERATURE AND BACKGROUND 71 4. PETRI NET SEMANTICS 73 4.1 COMPOSITIONALITY AND NETS 73 4.2 LABELLED NETS AND BOXES 75 4.2.1 AN EXAMPLE 75 4.2.2 ACTIONS AND RELABELLINGS 76 4.2.3 LABELLED NETS 77 4.2.4 EQUIVALENCE NOTIONS 82 4.2.5 BOXES 86 4.3 NET REFINEMENT 90 4.3.1 OPERATOR BOXES - 90 4.3.2 INTUITION BEHIND NET REFINEMENT 92 4.3.3 PLACE AND TRANSITION NAMES 95 4.3.4 FORMAL DEFINITION OF NET REFINEMENT 97 4.3.5 REMARKS ON NET REFINEMENT 99 4.3.6 PROPERTIES 101 4.3.7 DISCUSSION 103 4.4 PETRI NET SEMANTICS OF PBC 104 4.4.1 ELEMENTARY ACTIONS 106 4.4.2 PARALLEL COMPOSITION 106 4.4.3 CHOICE COMPOSITION 107 4.4.4 SEQUENTIAL COMPOSITION 109 4.4.5 BASIC RELABELLING 110 4.4.6 SYNCHRONISATION 110 4.4.7 RESTRICTION 119 4.4.8 SCOPING 120 4.4.9 ITERATION 120 4.4.10 DATA VARIABLES 123 4.4.11 GENERALISED CONTROL FLOW OPERATORS 124 4.4.12 GENERALISED COMMUNICATION INTERFACE OPERATORS 126 4.4.13 GENERALISED ITERATIONS 127 4.5 REFINED OPERATORS 129 4.6 LITERATURE AND BACKGROUND 132 5. ADDING RECURSION 133 5.1 INCLUSION ORDER ON LABELLED NETS 133 5.2 SOLVING RECURSIVE EQUATIONS 135 5.2.1 USING FIXPOINTS TO SOLVE RECURSIVE EQUATIONS 137 5.2.2 PLACES AND TRANSITIONS IN NET SOLUTIONS 140 5.2.3 AN EXAMPLE OF THE LIMIT CONSTRUCTION 144 CONTENTS IX 5.2.4 DERIVING SEED BOXES 145 5.2.5 A CLOSED FORM OF THE MAXIMAL SOLUTION 151 5.2.6 MINIMAL SOLUTIONS 153 5.3 FINITARY EQUATIONS AND FINITE OPERATOR BOXES 157 5.3.1 FINITARY EQUATION 157 5.3.2 FINITE OPERATOR BOX 159 5.4 FURTHER EXAMPLES 161 5.4.1 UNBOUNDED PARALLEL COMPOSITION 161 5.4.2 REAR-UNGUARDEDNESS 162 5.4.3 CONCURRENCY WITHIN UNBOUNDED CHOICE 164 5.4.4 EXTREME UNGUARDEDNESS 166 5.4.5 (NON)USE OF EMPTY NETS IN THE LIMIT CONSTRUCTION . . . 167 5.5 SOLVING SYSTEMS OF RECURSIVE EQUATIONS 167 5.5.1 APPROXIMATIONS, EXISTENCE, AND UNIQUENESS 168 5.5.2 A CLOSED FORM OF THE MAXIMAL SOLUTION 169 5.5.3 GUARDED SYSTEMS 171 5.6 LITERATURE AND BACKGROUND 172 6. S-INVARIANTS 173 6.1 S-INVARIANTS, S-COMPONENTS, AND S-AGGREGATES 174 6.1.1 S-INVARIANTS 176 6.1.2 S-COMPONENTS 181 6.1.3 S-AGGREGATES 182 6.2 THE SYNTHESIS PROBLEM FOR NET REFINEMENT 183 6.2.1 COMPOSING S-INVARIANTS 185 6.2.2 MULTIPLICATIVE DISTRIBUTION FUNCTIONS 190 6.2.3 EX-BINARY S-INVARIANTS 193 6.2.4 RATIONAL GROUPINGS 195 6.3 THE SYNTHESIS PROBLEM FOR RECURSIVE SYSTEMS 200 6.3.1 NAME TREES OF NETS IN THE MAXIMAL SOLUTION 201 6.3.2 COMPOSING S-INVARIANTS FOR RECURSIVE BOXES 202 6.3.3 COVERABILITY RESULTS 209 6.4 FINITE PRECEDENCE PROPERTIES 216 6.4.1 PROCESS SEMANTICS 218 6.4.2 FINITE PRECEDENCE OF EVENTS 222 6.4.3 FINITENESS OF COMPLETE PROCESSES 225 6.5 LITERATURE AND BACKGROUND 226 7. THE BOX ALGEBRA 227 7.1 SOS-OPERATOR BOXES 227 7.1.1 A RUNNING EXAMPLE 232 7.1.2 PROPERTIES OF FACTORISATIONS 232 7.1.3 THE DOMAIN OF APPLICATION OF AN SOS-OPERATOR BOX . . 234 7.1.4 STATIC PROPERTIES OF REFINEMENTS 235 7.1.5 MARKINGS OF NETS 239 X CONTENTS 7.2 STRUCTURED OPERATIONAL SEMANTICS OF COMPOSITE BOXES 241 7.2.1 SOUNDNESS . 243 7.2.2 SIMILARITY RELATION ON TUPLES OF BOXES 245 7.2.3 COMPLETENESS 248 7.2.4 SOLUTIONS OF RECURSIVE SYSTEMS 253 7.2.5 BEHAVIOURAL RESTRICTIONS 255 7.3 A PROCESS ALGEBRA AND ITS SEMANTICS 259 7.3.1 A RUNNING EXAMPLE: THE DIY ALGEBRA 262 7.3.2 INFINITE OPERATORS 264 7.3.3 DENOTATIONAL SEMANTICS 267 7.3.4 STRUCTURAL SIMILARITY RELATION ON EXPRESSIONS 270 7.3.5 TRANSITION-BASED OPERATIONAL SEMANTICS 279 7.3.6 CONSISTENCY OF THE TWO SEMANTICS 286 7.3.7 LABEL-BASED OPERATIONAL SEMANTICS 287 7.3.8 PARTIAL ORDER SEMANTICS OF BOX EXPRESSIONS 290 7.4 LITERATURE AND BACKGROUND 294 8. PBC AND OTHER PROCESS ALGEBRAS 295 8.1 (GENERALISED) PBC IS A BOX ALGEBRA 295 8.1.1 PBC WITHOUT LOOPS 295 8.1.2 SAFE TRANSLATION OF THE TERNARY PBC ITERATION 299 8.1.3 PBC WITH GENERALISED LOOPS 306 8.2 OTHER PROCESS ALGEBRAS 308 8.2.1 CCS 310 8.2.2 TCSP 311 8.2.3 COSY 311 8.3 LITERATURE AND BACKGROUND 312 9. A CONCURRENT PROGRAMMING LANGUAGE 313 9.1 SYNTAX OF RAZOR 313 9.1.1 PROGRAMS AND BLOCKS 315 9.1.2 DECLARATIONS 315 9.1.3 COMMANDS AND ACTIONS 316 9.1.4 GUARDED COMMANDS 316 9.1.5 EXPRESSIONS AND OPERATORS 317 9.1.6 SYNTACTIC VARIATIONS 317 9.2 SEMANTICS OF RAZOR 318 9.2.1 PROGRAMS, BLOCKS, AND DECLARATIONS 319 9.2.2 BASIC CHANNEL PROCESSES 321 9.2.3 COMMAND CONNECTIVES 324 9.2.4 ACTIONS AND GUARDED COMMANDS 325 9.3 THREE RAZOR PROGRAMS 329 9.4 ADDING RECURSIVE PROCEDURES 332 9.5 SOME CONSEQUENCES OF THE THEORY 336 CONTENTS XI 9.6 PROOFS OF DISTRIBUTED ALGORITHMS 340 9.6.1 A FINAL SET OF PETRI-NET-RELATED DEFINITIONS 340 9.6.2 PETERSON'S MUTUAL EXCLUSION ALGORITHM 342 9.6.3 DEKKER'S AND MORRIS'S MUTUAL EXCLUSION ALGORITHMS . . 346 9.7 LITERATURE AND BACKGROUND 347 10. CONCLUSION 34 9 APPENDIX: SOLUTIONS OF SELECTED EXERCISES 351 REFERENCES 362 INDEX 369
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spelling	Best, Eike 1951- Verfasser (DE-588)1021355593 aut Petri net algebra Eike Best ; Raymond Devillers ; Maciej Koutny Berlin [u.a.] Springer 2001 XI, 378 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs in theoretical computer science Ciência da computação larpcal Informatique - Mathématiques Parallélisme (Informatique) Petri netwerken gtt Redes de petri larpcal Álgebra larpcal Informatik Mathematik Computer science Mathematics Parallel processing (Electronic computers) Petri nets Prozessalgebra (DE-588)4283920-8 gnd rswk-swf Petri-Netz (DE-588)4045388-1 gnd rswk-swf Petri-Netz (DE-588)4045388-1 s Prozessalgebra (DE-588)4283920-8 s DE-604 Devillers, Raymond Verfasser aut Koutny, Maciej Verfasser aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009250590&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Best, Eike 1951- Devillers, Raymond Koutny, Maciej Petri net algebra Ciência da computação larpcal Informatique - Mathématiques Parallélisme (Informatique) Petri netwerken gtt Redes de petri larpcal Álgebra larpcal Informatik Mathematik Computer science Mathematics Parallel processing (Electronic computers) Petri nets Prozessalgebra (DE-588)4283920-8 gnd Petri-Netz (DE-588)4045388-1 gnd
subject_GND	(DE-588)4283920-8 (DE-588)4045388-1
title	Petri net algebra
title_auth	Petri net algebra
title_exact_search	Petri net algebra
title_full	Petri net algebra Eike Best ; Raymond Devillers ; Maciej Koutny
title_fullStr	Petri net algebra Eike Best ; Raymond Devillers ; Maciej Koutny
title_full_unstemmed	Petri net algebra Eike Best ; Raymond Devillers ; Maciej Koutny
title_short	Petri net algebra
title_sort	petri net algebra
topic	Ciência da computação larpcal Informatique - Mathématiques Parallélisme (Informatique) Petri netwerken gtt Redes de petri larpcal Álgebra larpcal Informatik Mathematik Computer science Mathematics Parallel processing (Electronic computers) Petri nets Prozessalgebra (DE-588)4283920-8 gnd Petri-Netz (DE-588)4045388-1 gnd
topic_facet	Ciência da computação Informatique - Mathématiques Parallélisme (Informatique) Petri netwerken Redes de petri Álgebra Informatik Mathematik Computer science Mathematics Parallel processing (Electronic computers) Petri nets Prozessalgebra Petri-Netz
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009250590&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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