Holdings: Fundamentals of algebraic graph transformation

Fundamentals of algebraic graph transformation:

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Bibliographic Details
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2006
Series:	Monographs in theoretical computer science
Subjects:	Grammaires de graphes Informatique - Mathématiques Categories (Mathematics) Graph grammars Graph theory Morphisms (Mathematics) Graphersetzungssystem Formale Spezifikationstechnik
Online Access:	Inhaltstext Inhaltsverzeichnis Inhaltsverzeichnis
Item Description:	Hier auch später erschienene, unveränderte Nachdrucke
Physical Description:	XIII, 388 S. Ill., graph. Darst.
ISBN:	3540311874 9783540311874 9783642068317

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245	1	0	\|a Fundamentals of algebraic graph transformation \|c H. Ehrig ...
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adam_text	H. EHRIG YY K. EHRIG U. PRANGE YY G. TAENTZER FUNDAMENTALS OF ALGEBRAIC GRAPH TRANSFORMATION WITH 41 FIGURES 4U SPRINGER CONTENTS PART I INTRODUCTIO N T O GRAPH TRANSFORMATION SYSTEM S 1 GENERAL INTRODUCTIO N 5 1.1 GENERAL OVERVIEW OF GRAPH GRAMMARS AND GRAPH TRANSFORMATION 5 1.1.1 WHAT IS GRAPH TRANSFORMATION? 6 1.1.2 AIMS AND PARADIGMS OF GRAPH TRANSFORMATION 6 1.1.3 OVERVIEW OF VARIOUS APPROACHES 9 1.2 THE MAIN IDEAS OF THE ALGEBRAIC GRAPH TRANSFORMATION APPROACH 10 1.2.1 THE DPO APPROACH 11 1.2.2 THE ALGEBRAIC ROOTS 12 1.2.3 PROM THE DPO TO THE SPO APPROACH 13 1.2.4 FROM GRAPHS T O HIGH-LEVEL STRUCTURES 14 1.3 THE CHAPTERS OF THIS BOOK AND THE MAIN RESULTS 15 1.3.1 PAR T I: INTRODUCTION T O GRAPH TRANSFORMATION SYSTEMS . 15 1.3.2 PART II: ADHESIVE HLR CATEGORIES AND SYSTEMS 15 1.3.3 PAR T III: TYPED ATTRIBUTED GRAPH TRANSFORMATION SYSTEMS 16 1.3.4 PAR T IV: CASE STUDY AND TOOL SUPPORT 17 1.3.5 APPENDICES 17 1.3.6 HINTS FOR READING THIS BOOK 17 1.4 BIBLIOGRAPHIC NOTES AND FURTHER TOPICS 17 1.4.1 CONCEPTS OF GRAPH GRAMMARS AND GRAPH TRANSFORMATION SYSTEMS 17 1.4.2 APPLICATION AREAS OF GRAPH TRANSFORMATION SYSTEMS .. . 19 1.4.3 LANGUAGES AND TOOLS FOR GRAPH TRANSFORMATION SYSTEMS 19 1.4.4 FUTURE WORK 20 X CONTENTS 2 GRAPHS , TYPE D GRAPHS , AN D TH E GLUIN G CONSTRUCTIO N 21 2.1 GRAPHS AND TYPED GRAPHS 21 2.2 INTRODUCTION TO CATEGORIES 25 2.3 PUSHOUTS AS A GLUING CONSTRUCTION 29 2.4 PULLBACKS AS THE DUAL CONSTRUCTION OF PUSHOUTS 33 3 GRAP H TRANSFORMATIO N SYSTEM S 37 3.1 BASIC DEFINITIONS FOR GT SYSTEMS 37 3.2 CONSTRUCTION OF GRAPH TRANSFORMATIONS 43 3.3 LOCAL (PHURCH-ROSSER AND PARALLELISM THEOREMS FOR GT SYSTEMS 47 3.4 OVERVIEW OF SOME OTHER MAIN RESULTS FOR GT SYSTEMS 53 3.4.1 CONCURRENCY THEOREM 54 3.4.2 EMBEDDING AND EXTENSION THEOREMS 56 3.4.3 CONFLUENCE, LOCAL CONFLUENCE, TERMINATION, AND CRITICAL PAIRS 59 3.4.4 FUNCTIONAL BEHAVIOR OF GT SYSTEMS AND TERMINATION ANALYSIS 62 3.5 GRAPH CONSTRAINTS AND APPLICATION CONDITIONS 64 PAR T II ADHESIV E HIGH-LEVE L REPLACEMEN T CATEGORIE S AN D SYSTEM S 4 ADHESIV E HIGH-LEVE L REPLACEMEN T CATEGORIE S 77 4.1 VAN KAMPEN SQUARES AND ADHESIVE CATEGORIES 77 4.2 ADHESIVE HLR CATEGORIES 86 4.3 HLR PROPERTIES OF ADHESIVE HLR CATEGORIES 96 5 ADHESIV E HIGH-LEVE L REPLACEMEN T SYSTEM S 101 5.1 BASIC CONCEPTS OF ADHESIVE HLR SYSTEMS 101 5.2 INSTANTIATION OF ADHESIVE HLR SYSTEMS 105 5.2.1 GRAPH AND TYPED GRAPH TRANSFORMATION SYSTEMS 106 5.2.2 HYPERGRAPH TRANSFORMATION SYSTEMS 106 5.2.3 PETR I NET TRANSFORMATION SYSTEMS 107 5.2.4 ALGEBRAIC SPECIFICATION TRANSFORMATION SYSTEMS 108 5.2.5 TYPED ATTRIBUTED GRAPH TRANSFORMATION SYSTEMS 108 5.3 THE LOCAL CHURCH-ROSSER AND PARALLELISM THEOREMS 109 5.4 CONCURRENCY THEOREM AND PAIR FACTORIZATION 117 6 EMBEDDIN G AN D LOCA L CONFLUENC E 125 6.1 INITIAL PUSHOUTS AND THE GLUING CONDITION 125 6.2 EMBEDDING AND EXTENSION THEOREMS 130 6.3 CRITICAL PAIRS 140 6.4 LOCAL CONFLUENCE THEOREM 144 CONTENTS XI CONSTRAINT S AND APPLICATIO N CONDITION S 151 7.1 DEFINITION OF CONSTRAINTS AND APPLICATION CONDITIONS 152 7.2 CONSTRUCTION OF APPLICATION CONDITIONS FROM CONSTRAINTS 156 7.3 CONSTRUCTION OF LEFT FROM RIGHT APPLICATION CONDITIONS 160 7.4 GUARANTEEING AND PRESERVATION OF CONSTRAINTS 164 PART II I TYPE D ATTRIBUTE D GRAPH TRANSFORMATION SYSTEM S 8 TYPE D ATTRIBUTE D GRAPHS 171 8.1 ATTRIBUTED GRAPHS AND TYPING 172 8.2 PUSHOUTS AS A GLUING CONSTRUCTION OF ATTRIBUTED GRAPHS 177 8.3 PULLBACKS OF ATTRIBUTED GRAPHS 178 9 TYPE D ATTRIBUTE D GRAPH TRANSFORMATION SYSTEM S 181 9.1 BASIC CONCEPTS FOR TYPED AGT SYSTEMS 181 9.2 CONSTRUCTION OF TYPED ATTRIBUTED GRAPH TRANSFORMATIONS ... . 188 9.3 LOCAL CHURCH-ROSSER AND PARALLELISM THEOREM FOR TYPED AGT SYSTEMS 190 9.4 CONCURRENCY THEOREM AND PAIR FACTORIZATION FOR TYPED AGT SYSTEMS 194 9.4.1 PAIR FACTORIZATIONS 194 9.4.2 CONCURRENCY THEOREM 201 10 EMBEDDIN G AND LOCAL CONFLUENCE FOR TYPE D AG T SYSTEM S 207 10.1 EMBEDDING AND EXTENSION THEOREMS FOR TYPED AGT SYSTEMS 207 10.2 CRITICAL PAIRS FOR TYPED AGT SYSTEMS 215 10.3 LOCAL CONFLUENCE THEOREM FOR TYPED AGT SYSTEMS 218 11 ADHESIV E HLR CATEGORIE S FOR TYPE D ATTRIBUTE D GRAPHS .. . 221 11.1 ATTRIBUTED GRAPH STRUCTURE SIGNATURES AND TYPED ATTRIBUTED GRAPHS 222 11.2 DEFINITION OF CONCRETE ADHESIVE HLR CATEGORIES 225 11.3 VERIFICATION OF THE MAIN RESULTS FOR TYPED AGT SYSTEMS 232 12 CONSTRAINTS , APPLICATIO N CONDITION S AND TERMINATIO N FOR TAG T SYSTEM S 237 12.1 CONSTRAINTS AND APPLICATION CONDITIONS FOR TYPED AGT SYSTEMS 237 12.2 EQUIVALENCE OF CONSTRAINTS AND APPLICATION CONDITIONS 242 12.3 TERMINATION CRITERIA FOR LAYERED TYPED ATTRIBUTED GRAPH GRAMMARS 249 XII CONTENTS 13 TYPE D ATTRIBUTE D GRAPH TRANSFORMATION WIT H INHERITANCE . 259 13.1 ATTRIBUTED TYPE GRAPHS WITH INHERITANCE 260 13.2 ATTRIBUTED CLAN MORPHISMS 265 13.3 PRODUCTIONS AND ATTRIBUTED GRAPH TRANSFORMATION WITH INHERITANCE 271 13.4 EQUIVALENCE OF CONCEPTS WITH AND WITHOUT INHERITANCE 278 PART IV CASE STUD Y O N MODE L TRANSFORMATION, AND TOOL SUPPORT PR AGG I 14 CASE STUD Y O N MODE L TRANSFORMATION 287 14.1 MODEL TRANSFORMATION BY TYPED ATTRIBUTED GRAPH TRANSFORMATION 287 14.2 MODEL TRANSFORMATION FROM STATECHARTS T O PETRI NETS 288 14.2.1 SOURCE MODELING LANGUAGE: SIMPLE VERSION OF UML STATECHARTS 289 14.2.2 TARGET MODELING LANGUAGE: PETRI NETS 290 14.2.3 MODEL TRANSFORMATION 293 14.2.4 TERMINATION ANALYSIS OF THE MODEL TRANSFORMATION ... . 301 14.3 FURTHER CASE STUDIES 303 14.3.1 FROM THE GENERAL RESOURCE MODEL TO PETRI NETS 303 14.3.2 FROM PROCESS INTERACTION DIAGRAMS TO TIMED PETRI NETS 304 14.4 CONCLUSION 304 15 IMPLEMENTATIO N OF TYPE D ATTRIBUTE D GRAPH TRANSFORMATION BY AGG 305 15.1 LANGUAGE CONCEPTS OF AGG 305 15.1.1 GRAPHS 306 15.1.2 TYPING FACILITIES 306 15.1.3 NODE AND EDGE ATTRIBUTES 307 15.1.4 RULES AND MATCHES 308 15.1.5 GRAPH TRANSFORMATIONS 310 15.1.6 GRAPH GRAMMARS 312 15.2 ANALYSIS TECHNIQUES IMPLEMENTED IN AGG 312 15.2.1 GRAPH CONSTRAINTS 312 15.2.2 CRITICAL PAIR ANALYSIS 313 15.2.3 GRAPH PARSING 317 15.2.4 TERMINATION 318 15.3 TOOL ENVIRONMENT OF AGG 318 15.3.1 VISUAL ENVIRONMENT 320 15.3.2 GRAPH TRANSFORMATION ENGINE 321 15.3.3 TOOL INTEGRATION 322 15.4 CONCLUSION 322 CONTENTS XIII APPENDICE S A A SHORT INTRODUCTIO N T O CATEGOR Y THEOR Y 329 A.I CATEGORIES 329 A.2 CONSTRUCTION OF CATEGORIES, AND DUALITY 330 A.3 MONOMORPHISMS, EPIMORPHISMS, AND ISOMORPHISMS 332 A.4 PUSHOUTS AND PULLBACKS 334 A.5 BINARY COPRODUCTS AND INITIAL OBJECTS 340 A.6 FUNCTORS, FUNCTOR CATEGORIES, AND COMMA CATEGORIES 344 A.7 ISOMORPHISM AND EQUIVALENCE OF CATEGORIES 350 B A SHORT INTRODUCTIO N T O SIGNATURE S AND ALGEBRA S 353 B.I ALGEBRAIC SIGNATURES 353 B.2 ALGEBRAS 355 B.3 TERMS AND TERM EVALUATION 357 C DETAILE D PROOF S 359 C.I COMPLETION OF PROOF OF FACT 4.24 359 C.2 PROOF OF LEMMA 6.25 361 C.3 COMPLETION OF PROOF OF THEOREM 11.3 362 C.3.1 WELL-DEFINEDNESS 362 C.3.2 FUNCTORS 364 C.3.3 ISOMORPHISM 365 C.4 PROOF OF LEMMA 11.17 366 C.4.1 WELL-DEFINEDNESS 366 C.4.2 PUSHOUT PROPERTY 367 C.4.3 INITIAL PUSHOUT 368 C.5 PROOF OF THEOREM 13.12 370 C.6 PROOF OF LEMMA 13.20 373 REFERENCES 377 INDE X 385
adam_txt	H. EHRIG YY K. EHRIG U. PRANGE YY G. TAENTZER FUNDAMENTALS OF ALGEBRAIC GRAPH TRANSFORMATION WITH 41 FIGURES 4U SPRINGER CONTENTS PART I INTRODUCTIO N T O GRAPH TRANSFORMATION SYSTEM S 1 GENERAL INTRODUCTIO N 5 1.1 GENERAL OVERVIEW OF GRAPH GRAMMARS AND GRAPH TRANSFORMATION 5 1.1.1 WHAT IS GRAPH TRANSFORMATION? 6 1.1.2 AIMS AND PARADIGMS OF GRAPH TRANSFORMATION 6 1.1.3 OVERVIEW OF VARIOUS APPROACHES 9 1.2 THE MAIN IDEAS OF THE ALGEBRAIC GRAPH TRANSFORMATION APPROACH 10 1.2.1 THE DPO APPROACH 11 1.2.2 THE ALGEBRAIC ROOTS 12 1.2.3 PROM THE DPO TO THE SPO APPROACH 13 1.2.4 FROM GRAPHS T O HIGH-LEVEL STRUCTURES 14 1.3 THE CHAPTERS OF THIS BOOK AND THE MAIN RESULTS 15 1.3.1 PAR T I: INTRODUCTION T O GRAPH TRANSFORMATION SYSTEMS . 15 1.3.2 PART II: ADHESIVE HLR CATEGORIES AND SYSTEMS 15 1.3.3 PAR T III: TYPED ATTRIBUTED GRAPH TRANSFORMATION SYSTEMS 16 1.3.4 PAR T IV: CASE STUDY AND TOOL SUPPORT 17 1.3.5 APPENDICES 17 1.3.6 HINTS FOR READING THIS BOOK 17 1.4 BIBLIOGRAPHIC NOTES AND FURTHER TOPICS 17 1.4.1 CONCEPTS OF GRAPH GRAMMARS AND GRAPH TRANSFORMATION SYSTEMS 17 1.4.2 APPLICATION AREAS OF GRAPH TRANSFORMATION SYSTEMS . . 19 1.4.3 LANGUAGES AND TOOLS FOR GRAPH TRANSFORMATION SYSTEMS 19 1.4.4 FUTURE WORK 20 X CONTENTS 2 GRAPHS , TYPE D GRAPHS , AN D TH E GLUIN G CONSTRUCTIO N 21 2.1 GRAPHS AND TYPED GRAPHS 21 2.2 INTRODUCTION TO CATEGORIES 25 2.3 PUSHOUTS AS A GLUING CONSTRUCTION 29 2.4 PULLBACKS AS THE DUAL CONSTRUCTION OF PUSHOUTS 33 3 GRAP H TRANSFORMATIO N SYSTEM S 37 3.1 BASIC DEFINITIONS FOR GT SYSTEMS 37 3.2 CONSTRUCTION OF GRAPH TRANSFORMATIONS 43 3.3 LOCAL (PHURCH-ROSSER AND PARALLELISM THEOREMS FOR GT SYSTEMS 47 3.4 OVERVIEW OF SOME OTHER MAIN RESULTS FOR GT SYSTEMS 53 3.4.1 CONCURRENCY THEOREM 54 3.4.2 EMBEDDING AND EXTENSION THEOREMS 56 3.4.3 CONFLUENCE, LOCAL CONFLUENCE, TERMINATION, AND CRITICAL PAIRS 59 3.4.4 FUNCTIONAL BEHAVIOR OF GT SYSTEMS AND TERMINATION ANALYSIS 62 3.5 GRAPH CONSTRAINTS AND APPLICATION CONDITIONS 64 PAR T II ADHESIV E HIGH-LEVE L REPLACEMEN T CATEGORIE S AN D SYSTEM S 4 ADHESIV E HIGH-LEVE L REPLACEMEN T CATEGORIE S 77 4.1 VAN KAMPEN SQUARES AND ADHESIVE CATEGORIES 77 4.2 ADHESIVE HLR CATEGORIES 86 4.3 HLR PROPERTIES OF ADHESIVE HLR CATEGORIES 96 5 ADHESIV E HIGH-LEVE L REPLACEMEN T SYSTEM S 101 5.1 BASIC CONCEPTS OF ADHESIVE HLR SYSTEMS 101 5.2 INSTANTIATION OF ADHESIVE HLR SYSTEMS 105 5.2.1 GRAPH AND TYPED GRAPH TRANSFORMATION SYSTEMS 106 5.2.2 HYPERGRAPH TRANSFORMATION SYSTEMS 106 5.2.3 PETR I NET TRANSFORMATION SYSTEMS 107 5.2.4 ALGEBRAIC SPECIFICATION TRANSFORMATION SYSTEMS 108 5.2.5 TYPED ATTRIBUTED GRAPH TRANSFORMATION SYSTEMS 108 5.3 THE LOCAL CHURCH-ROSSER AND PARALLELISM THEOREMS 109 5.4 CONCURRENCY THEOREM AND PAIR FACTORIZATION 117 6 EMBEDDIN G AN D LOCA L CONFLUENC E 125 6.1 INITIAL PUSHOUTS AND THE GLUING CONDITION 125 6.2 EMBEDDING AND EXTENSION THEOREMS 130 6.3 CRITICAL PAIRS 140 6.4 LOCAL CONFLUENCE THEOREM 144 CONTENTS XI CONSTRAINT S AND APPLICATIO N CONDITION S 151 7.1 DEFINITION OF CONSTRAINTS AND APPLICATION CONDITIONS 152 7.2 CONSTRUCTION OF APPLICATION CONDITIONS FROM CONSTRAINTS 156 7.3 CONSTRUCTION OF LEFT FROM RIGHT APPLICATION CONDITIONS 160 7.4 GUARANTEEING AND PRESERVATION OF CONSTRAINTS 164 PART II I TYPE D ATTRIBUTE D GRAPH TRANSFORMATION SYSTEM S 8 TYPE D ATTRIBUTE D GRAPHS 171 8.1 ATTRIBUTED GRAPHS AND TYPING 172 8.2 PUSHOUTS AS A GLUING CONSTRUCTION OF ATTRIBUTED GRAPHS 177 8.3 PULLBACKS OF ATTRIBUTED GRAPHS 178 9 TYPE D ATTRIBUTE D GRAPH TRANSFORMATION SYSTEM S 181 9.1 BASIC CONCEPTS FOR TYPED AGT SYSTEMS 181 9.2 CONSTRUCTION OF TYPED ATTRIBUTED GRAPH TRANSFORMATIONS . . 188 9.3 LOCAL CHURCH-ROSSER AND PARALLELISM THEOREM FOR TYPED AGT SYSTEMS 190 9.4 CONCURRENCY THEOREM AND PAIR FACTORIZATION FOR TYPED AGT SYSTEMS 194 9.4.1 PAIR FACTORIZATIONS 194 9.4.2 CONCURRENCY THEOREM 201 10 EMBEDDIN G AND LOCAL CONFLUENCE FOR TYPE D AG T SYSTEM S 207 10.1 EMBEDDING AND EXTENSION THEOREMS FOR TYPED AGT SYSTEMS 207 10.2 CRITICAL PAIRS FOR TYPED AGT SYSTEMS 215 10.3 LOCAL CONFLUENCE THEOREM FOR TYPED AGT SYSTEMS 218 11 ADHESIV E HLR CATEGORIE S FOR TYPE D ATTRIBUTE D GRAPHS . . 221 11.1 ATTRIBUTED GRAPH STRUCTURE SIGNATURES AND TYPED ATTRIBUTED GRAPHS 222 11.2 DEFINITION OF CONCRETE ADHESIVE HLR CATEGORIES 225 11.3 VERIFICATION OF THE MAIN RESULTS FOR TYPED AGT SYSTEMS 232 12 CONSTRAINTS , APPLICATIO N CONDITION S AND TERMINATIO N FOR TAG T SYSTEM S 237 12.1 CONSTRAINTS AND APPLICATION CONDITIONS FOR TYPED AGT SYSTEMS 237 12.2 EQUIVALENCE OF CONSTRAINTS AND APPLICATION CONDITIONS 242 12.3 TERMINATION CRITERIA FOR LAYERED TYPED ATTRIBUTED GRAPH GRAMMARS 249 XII CONTENTS 13 TYPE D ATTRIBUTE D GRAPH TRANSFORMATION WIT H INHERITANCE . 259 13.1 ATTRIBUTED TYPE GRAPHS WITH INHERITANCE 260 13.2 ATTRIBUTED CLAN MORPHISMS 265 13.3 PRODUCTIONS AND ATTRIBUTED GRAPH TRANSFORMATION WITH INHERITANCE 271 13.4 EQUIVALENCE OF CONCEPTS WITH AND WITHOUT INHERITANCE 278 PART IV CASE STUD Y O N MODE L TRANSFORMATION, AND TOOL SUPPORT \PR AGG I 14 CASE STUD Y O N MODE L TRANSFORMATION 287 14.1 MODEL TRANSFORMATION BY TYPED ATTRIBUTED GRAPH TRANSFORMATION 287 14.2 MODEL TRANSFORMATION FROM STATECHARTS T O PETRI NETS 288 14.2.1 SOURCE MODELING LANGUAGE: SIMPLE VERSION OF UML STATECHARTS 289 14.2.2 TARGET MODELING LANGUAGE: PETRI NETS 290 14.2.3 MODEL TRANSFORMATION 293 14.2.4 TERMINATION ANALYSIS OF THE MODEL TRANSFORMATION . . 301 14.3 FURTHER CASE STUDIES 303 14.3.1 FROM THE GENERAL RESOURCE MODEL TO PETRI NETS 303 14.3.2 FROM PROCESS INTERACTION DIAGRAMS TO TIMED PETRI NETS 304 14.4 CONCLUSION 304 15 IMPLEMENTATIO N OF TYPE D ATTRIBUTE D GRAPH TRANSFORMATION BY AGG 305 15.1 LANGUAGE CONCEPTS OF AGG 305 15.1.1 GRAPHS 306 15.1.2 TYPING FACILITIES 306 15.1.3 NODE AND EDGE ATTRIBUTES 307 15.1.4 RULES AND MATCHES 308 15.1.5 GRAPH TRANSFORMATIONS 310 15.1.6 GRAPH GRAMMARS 312 15.2 ANALYSIS TECHNIQUES IMPLEMENTED IN AGG 312 15.2.1 GRAPH CONSTRAINTS 312 15.2.2 CRITICAL PAIR ANALYSIS 313 15.2.3 GRAPH PARSING 317 15.2.4 TERMINATION 318 15.3 TOOL ENVIRONMENT OF AGG 318 15.3.1 VISUAL ENVIRONMENT 320 15.3.2 GRAPH TRANSFORMATION ENGINE 321 15.3.3 TOOL INTEGRATION 322 15.4 CONCLUSION 322 CONTENTS XIII APPENDICE S A A SHORT INTRODUCTIO N T O CATEGOR Y THEOR Y 329 A.I CATEGORIES 329 A.2 CONSTRUCTION OF CATEGORIES, AND DUALITY 330 A.3 MONOMORPHISMS, EPIMORPHISMS, AND ISOMORPHISMS 332 A.4 PUSHOUTS AND PULLBACKS 334 A.5 BINARY COPRODUCTS AND INITIAL OBJECTS 340 A.6 FUNCTORS, FUNCTOR CATEGORIES, AND COMMA CATEGORIES 344 A.7 ISOMORPHISM AND EQUIVALENCE OF CATEGORIES 350 B A SHORT INTRODUCTIO N T O SIGNATURE S AND ALGEBRA S 353 B.I ALGEBRAIC SIGNATURES 353 B.2 ALGEBRAS 355 B.3 TERMS AND TERM EVALUATION 357 C DETAILE D PROOF S 359 C.I COMPLETION OF PROOF OF FACT 4.24 359 C.2 PROOF OF LEMMA 6.25 361 C.3 COMPLETION OF PROOF OF THEOREM 11.3 362 C.3.1 WELL-DEFINEDNESS 362 C.3.2 FUNCTORS 364 C.3.3 ISOMORPHISM 365 C.4 PROOF OF LEMMA 11.17 366 C.4.1 WELL-DEFINEDNESS 366 C.4.2 PUSHOUT PROPERTY 367 C.4.3 INITIAL PUSHOUT 368 C.5 PROOF OF THEOREM 13.12 370 C.6 PROOF OF LEMMA 13.20 373 REFERENCES 377 INDE X 385
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id	DE-604.BV021575831
illustrated	Illustrated
index_date	2024-07-02T14:40:00Z
indexdate	2024-07-09T20:39:01Z
institution	BVB
isbn	3540311874 9783540311874 9783642068317
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-014791577
oclc_num	181533205
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owner	DE-703 DE-29T DE-706 DE-384 DE-634 DE-83 DE-473 DE-BY-UBG DE-898 DE-BY-UBR
owner_facet	DE-703 DE-29T DE-706 DE-384 DE-634 DE-83 DE-473 DE-BY-UBG DE-898 DE-BY-UBR
physical	XIII, 388 S. Ill., graph. Darst.
publishDate	2006
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publisher	Springer
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series2	Monographs in theoretical computer science
spelling	Fundamentals of algebraic graph transformation H. Ehrig ... Berlin [u.a.] Springer 2006 XIII, 388 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs in theoretical computer science Hier auch später erschienene, unveränderte Nachdrucke Grammaires de graphes Informatique - Mathématiques Categories (Mathematics) Graph grammars Graph theory Morphisms (Mathematics) Graphersetzungssystem (DE-588)4274073-3 gnd rswk-swf Formale Spezifikationstechnik (DE-588)4299725-2 gnd rswk-swf Graphersetzungssystem (DE-588)4274073-3 s Formale Spezifikationstechnik (DE-588)4299725-2 s DE-604 Ehrig, Hartmut 1944-2016 Sonstige (DE-588)107905582 oth Erscheint auch als Online-Ausgabe 978-3-540-31188-1 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2760853&prov=M&dok_var=1&dok_ext=htm Inhaltstext http://www3.ub.tu-berlin.de/ihv/001708242.pdf Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014791577&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Fundamentals of algebraic graph transformation Grammaires de graphes Informatique - Mathématiques Categories (Mathematics) Graph grammars Graph theory Morphisms (Mathematics) Graphersetzungssystem (DE-588)4274073-3 gnd Formale Spezifikationstechnik (DE-588)4299725-2 gnd
subject_GND	(DE-588)4274073-3 (DE-588)4299725-2
title	Fundamentals of algebraic graph transformation
title_auth	Fundamentals of algebraic graph transformation
title_exact_search	Fundamentals of algebraic graph transformation
title_exact_search_txtP	Fundamentals of algebraic graph transformation
title_full	Fundamentals of algebraic graph transformation H. Ehrig ...
title_fullStr	Fundamentals of algebraic graph transformation H. Ehrig ...
title_full_unstemmed	Fundamentals of algebraic graph transformation H. Ehrig ...
title_short	Fundamentals of algebraic graph transformation
title_sort	fundamentals of algebraic graph transformation
topic	Grammaires de graphes Informatique - Mathématiques Categories (Mathematics) Graph grammars Graph theory Morphisms (Mathematics) Graphersetzungssystem (DE-588)4274073-3 gnd Formale Spezifikationstechnik (DE-588)4299725-2 gnd
topic_facet	Grammaires de graphes Informatique - Mathématiques Categories (Mathematics) Graph grammars Graph theory Morphisms (Mathematics) Graphersetzungssystem Formale Spezifikationstechnik
url	http://deposit.dnb.de/cgi-bin/dokserv?id=2760853&prov=M&dok_var=1&dok_ext=htm http://www3.ub.tu-berlin.de/ihv/001708242.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014791577&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT ehrighartmut fundamentalsofalgebraicgraphtransformation

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