Holdings: Parity games, separations, and the modal μ-calculus

Parity games, separations, and the modal μ-calculus:

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Bibliographic Details
Main Author:	Dittmann, Christoph (Author)
Format:	Thesis Electronic eBook
Language:	English
Published:	Berlin Universitätsverlag der TU Berlin 2017
Series:	Foundations of computing 9
Subjects:	Paritätsspiel My-Kalkül Hochschulschrift
Online Access:	Inhaltsverzeichnis Volltext Volltext Volltext Inhaltsverzeichnis
Physical Description:	1 Online-Ressource (x, 274 Seiten) Diagramme 21 cm
ISBN:	9783798328884
DOI:	10.14279/depositonce-5700

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Record in the Search Index

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adam_text	CONTENTS 1 INTRODUCTION 1 2 PRELIMINARIES 11 3 THE MODAL /X-CALCULUS AND PARITY GAMES 15 3.1 THE MODAL //-C ALCU LU S ........................................ 16 3.1.1 S Y N TAX ....................................................... 16 3.1.2 S EM ANTICS ................................................. 18 3.1.3 NEGATION NORMAL FORM ......................... 23 3.1.4 R ECU RSIO N ................................................. 26 3.1.5 E X A M P LE S ................................................. 28 3.1.6 BISIMULATION IN V A RIA N C E ......................... 31 3.1.7 SUBFORMULAS AND CLOSURE ...................... 34 3.1.8 FORMULA D E P TH ........................................ 38 3.2 PARITY G A M E S ....................................................... 47 3.2.1 D EFINITION ................................................. 47 3.2.2 POSITIONAL D E TE RM IN A C Y ......................... 50 3.2.3 ATTRACTOR SETS ........................................ 53 3.3 RELATION TO THE MODAL / C ALCULUS....................... 58 3.3.1 ANNOTATED F O RM U LA S............................... 59 3.3.2 MODEL-CHECKING G A M E ............................ 60 4 COMPUTATIONAL COMPLEXITY 71 4.1 THE COMPLEXITY OF PARITY G A M E S ...................... 71 4.1.1 GENERAL ALGORITHMS ............................... 74 4.1.2 ALGORITHMS ON RESTRICTED CLASSES .... 77 4.1.3 FIXED-PARAMETER T RA C TA B ILITY ............... 78 4.2 THE MODEL-CHECKING P RO B LE M ...................... 81 4.3 DIFFICULTY OF RESTRICTED C LA S S E S ......................... 83 4.3.1 HARDNESS ................................................. 84 4.3.2 PLANAR G R A P H S ........................................ 85 4.3.3 T REEW IDTH ................................................. 91 4.3.4 LOCALLY BOUNDED T REEW ID TH ................... 94 5 TYPES 99 5.1 A FEFERMAN-VAUGHT T H E O RE M ............................ 99 5.1.1 DIRECTED S EPARATIONS...................................101 5.2 PROOF OF THE MAIN T H E O RE M ...................................104 5.2.1 AN EASY G ASE............................................... 104 5.2.2 A SLIGHTLY MORE GENERAL G ASE ................... 106 5.2.3 PRIORITY T RACKING.........................................111 5.2.4 THE GENERAL GASE ......................................114 5.2.5 PARITY G A M E S............................................... 115 5.2.6 PROFILES AND T Y P E S ......................................116 5.2.7 DEFMABLE PROFILES.........................................126 5.2.8 A SMALL PARITY G A M E ................................132 5.2.9 FINISHING THE P RO O F......................................137 5.3 RUNNING TIME ........................................................ 140 5.3.1 UPPER B O U N D ............................................... 140 5.3.2 LOWER B O U N D ............................................... 145 5.4 FPT ALGORITHMS FOR MODEL CHECKING .... 147 5.4.1 WEAK SEPARATIONS ......................................147 5.4.2 KELLY-WIDTH ............................................... 152 5.4.3 D A G -W IDTH...................................................157 5.5 C ONCLUSIONS............................................................... 161 6 GRAPH OPERATIONS ON PARITY GAMES 163 6.1 P RELIM IN ARIES ........................................................... 164 6.1.1 BASIC D EFINITIONS.........................................164 6.1.2 HALF-SOLVING PARITY GAMES ........................166 6.1.3 RECOGNIZING WINNING R EGIONS ................... 169 6.2 THE JOIN OF TWO PARITY G A M E S ............................ 169 6.2.1 ADJOINING VERTICES BELONGING TO ONE PLAYER 171 6.2.2 JOINING TWO PARITY GAMES ........................180 6.3 PASTING OF PARITY G A M E S.........................................183 6.4 ADDING A SINGLE V ERTEX............................................187 6.5 C ONCLUSIONS .............................................................. 189 7 A FORMAL PROOF OF POSITIONAL DETERMINACY 191 7.1 B ACKGROUND .............................................................. 192 7.1.1 FORMAL P ROOFS...............................................192 7.1.2 COMPUTER-ASSISTED P RO O FS ..........................193 7.1.3 ISABELLE/H O L ...............................................194 7.2 THE INFORMAL P RO O F..................................................196 7.3 ISABELLE P R I M E R ........................................................202 7.3.1 S Y N TAX ........................................................... 202 7.3.2 G O N TE X T........................................................ 203 7.3.3 ADDING NEW F A C T S ..................................... 205 7.3.4 SOLVING G O A LS ...............................................205 7.3.5 A SSU M P TIO N S...............................................206 7.3.6 PROVING F A C TS ...............................................208 7.3.7 PROOF M E TH O D S ............................................210 7.3.8 RULES ........................................................... 212 7.3.9 NAMING F A C TS ...............................................213 7.3.10 FINDING F A C TS ...............................................214 7.3.11 QUANTIFICATION ............................................215 7.3.12 T Y P E S ........................................................... 219 7.3.13 EXPLORING F A C TS ............................................220 7.3.14 DEFINITIONS .................................................. 221 7.3.15 LOCALES ........................................................ 223 7.3.16 FURTHER R E A D IN G .........................................224 7.4 THE FORMAL PROOF .................................................. 226 7.5 TECHNICAL A SPECTS ..................................................... 228 7.5.1 GRAPHS ........................................................ 228 7.5.2 P A T H S ........................................................... 231 7.5.3 WELL-ORDERED S TRA TE G IE S ............................ 235 7.6 C ONCLUSIONS .............................................................. 239 7.6.1 TIME C OM PLEXITY.........................................239 7.6.2 TURING M AC H IN E S.........................................240 7.6.3 RESTRICTED GRAPH C LA S S E S ......................... 242 BIBLIOGRAPHY 243 INDEX 265 SYMBOLS 271
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spelling	Dittmann, Christoph Verfasser (DE-588)1159925909 aut Parity games, separations, and the modal μ-calculus Christoph Dittmann Berlin Universitätsverlag der TU Berlin 2017 1 Online-Ressource (x, 274 Seiten) Diagramme 21 cm txt rdacontent c rdamedia cr rdacarrier Foundations of computing 9 Dissertation Technische Universität Berlin 2017 Paritätsspiel (DE-588)1141802864 gnd rswk-swf My-Kalkül (DE-588)4530731-3 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content My-Kalkül (DE-588)4530731-3 s Paritätsspiel (DE-588)1141802864 s DE-604 Technische Universität Berlin Universitätsbibliothek (DE-588)5053182-7 pbl Erscheint auch als Druck-Ausgae 978-3-7983-2887-7 (DE-604)BV044946663 Foundations of computing 9 (DE-604)BV044943050 9 B:DE-101 application/pdf http://d-nb.info/1127244396/04 Inhaltsverzeichnis https://depositonce.tu-berlin.de/bitstream/11303/6135/3/dittmann_christoph.pdf Volltext https://depositonce.tu-berlin.de/handle/11303/6135 Volltext https://doi.org/10.14279/depositonce-5700 Resolving-System kostenfrei Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030042777&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Dittmann, Christoph Parity games, separations, and the modal μ-calculus Foundations of computing Paritätsspiel (DE-588)1141802864 gnd My-Kalkül (DE-588)4530731-3 gnd
subject_GND	(DE-588)1141802864 (DE-588)4530731-3 (DE-588)4113937-9
title	Parity games, separations, and the modal μ-calculus
title_auth	Parity games, separations, and the modal μ-calculus
title_exact_search	Parity games, separations, and the modal μ-calculus
title_full	Parity games, separations, and the modal μ-calculus Christoph Dittmann
title_fullStr	Parity games, separations, and the modal μ-calculus Christoph Dittmann
title_full_unstemmed	Parity games, separations, and the modal μ-calculus Christoph Dittmann
title_short	Parity games, separations, and the modal μ-calculus
title_sort	parity games separations and the modal μ calculus
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