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