Graph Structure And Monadic Second Order Logic
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Graph Structure And Monadic Second Order Logic
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Author : Bruno Courcelle
language : en
Publisher: Cambridge University Press
Release Date : 2012-06-14
Graph Structure And Monadic Second Order Logic written by Bruno Courcelle and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-14 with Mathematics categories.
The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The authors not only provide a thorough description of the theory, but also detail its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.
Graph Structure And Monadic Second Order Logic
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Author : B. Courcelle
language : en
Publisher:
Release Date : 2012
Graph Structure And Monadic Second Order Logic written by B. Courcelle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Logic, Symbolic and mathematical categories.
"The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The author not only provides a thorough description of the theory, but also details its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory"--
Graph Structure And Monadic Second Order Logic A Language Theoretic Approach
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Author : Bruno; Engelfriet Courcelle (Joost)
language : en
Publisher:
Release Date : 2012
Graph Structure And Monadic Second Order Logic A Language Theoretic Approach written by Bruno; Engelfriet Courcelle (Joost) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
Graph Structure And Monadic Second Order Logic
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Author : Bruno Courcelle
language : en
Publisher: Cambridge University Press
Release Date : 2012-06-14
Graph Structure And Monadic Second Order Logic written by Bruno Courcelle and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-14 with Mathematics categories.
The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The authors not only provide a thorough description of the theory, but also detail its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.
Nowhere Dense Classes Of Graphs
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Author : Siebertz, Sebastian
language : en
Publisher: Universitätsverlag der TU Berlin
Release Date : 2016-05-24
Nowhere Dense Classes Of Graphs written by Siebertz, Sebastian and has been published by Universitätsverlag der TU Berlin this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-24 with Computers categories.
We show that every first-order property of graphs can be decided in almost linear time on every nowhere dense class of graphs. For graph classes closed under taking subgraphs, our result is optimal (under a standard complexity theoretic assumption): it was known before that for all classes C of graphs closed under taking subgraphs, if deciding first-order properties of graphs in C is fixed-parameter tractable, parameterized by the length of the input formula, then C must be nowhere dense. Nowhere dense graph classes form a large variety of classes of sparse graphs including the class of planar graphs, actually all classes with excluded minors, and also bounded degree graphs and graph classes of bounded expansion. For our proof, we provide two new characterisations of nowhere dense classes of graphs. The first characterisation is in terms of a game, which explains the local structure of graphs from nowhere dense classes. The second characterisation is by the existence of sparse neighbourhood covers. On the logical side, we prove a rank-preserving version of Gaifman's locality theorem. The characterisation by neighbourhood covers is based on a characterisation of nowhere dense classes by generalised colouring numbers. We show several new bounds for the generalised colouring numbers on restricted graph classes, such as for proper minor closed classes and for planar graphs. Finally, we study the parameterized complexity of the first-order model-checking problem on structures where an ordering is available to be used in formulas. We show that first-order logic on ordered structures as well as on structures with a successor relation is essentially intractable on nearly all interesting classes. On the other hand, we show that the model-checking problem of order-invariant monadic second-order logic is tractable essentially on the same classes as plain monadic second-order logic and that the model-checking problem for successor-invariant first-order logic is tractable on planar graphs. Wir zeigen, dass jede Eigenschaft von Graphen aus einer nowhere dense Klasse von Graphen, die in der Präadikatenlogik formuliert werden kann, in fast linearer Zeit entschieden werden kann. Dieses Ergebnis ist optimal für Klassen von Graphen, die unter Subgraphen abgeschlossen sind (unter einer Standardannahme aus der Komplexitätstheorie). Um den obigen Satz zu beweisen, führen wir zwei neue Charakterisierungen von nowhere dense Klassen von Graphen ein. Zunächst charakterisieren wir solche Klassen durch ein Spiel, das die lokalen Eigenschaften von Graphen beschreibt. Weiter zeigen wir, dass eine Klasse, die unter Subgraphen abgeschlossen ist, genau dann nowhere dense ist, wenn alle lokalen Nachbarschaften von Graphen der Klasse dünn überdeckt werden können. Weiterhin beweisen wir eine erweiterte Version von Gaifman's Lokalitätssatz für die Prädikatenlogik, der eine Übersetzung von Formeln in lokale Formeln des gleichen Ranges erlaubt. In Kombination erlauben diese neuen Charakterisierungen einen effizienten, rekursiven Lösungsansatz für das Model-Checking Problem der Prädikatenlogik. Die Charakterisierung der nowhere dense Graphklassen durch die oben beschriebenen Überdeckungen basiert auf einer bekannten Charakterisierung durch verallgemeinerte Färbungszahlen. Unser Studium dieser Zahlen führt zu neuen, verbesserten Schranken für die verallgemeinerten Färbungszahlen von nowhere dense Klassen von Graphen, insbesondere für einige wichtige Subklassen, z. B. für Klassen mit ausgeschlossenen Minoren und für planare Graphen. Zuletzt untersuchen wir, welche Auswirkungen eine Erweiterung der Logik durch Ordnungs- bzw. Nachfolgerrelationen auf die Komplexität des Model-Checking Problems hat. Wir zeigen, dass das Problem auf fast allen interessanten Klassen nicht effizient gelöst werden kann, wenn eine beliebige Ordnungs- oder Nachfolgerrelation zum Graphen hinzugefügt wird. Andererseits zeigen wir, dass das Problem für ordnungsinvariante monadische Logik zweiter Stufe auf allen Klassen, für die bekannt ist, dass es für monadische Logik zweiter Stufe effizient gelöst werden kann, auch effizient gelöst werden kann. Wir zeigen, dass das Problem für nachfolgerinvariante Prädikatenlogik auf planaren Graphen effizient gelöst werden kann.
Handbook Of Graph Grammars And Computing By Graph Transformation
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Author : Grzegorz Rozenberg
language : en
Publisher: World Scientific
Release Date : 1997-01-01
Handbook Of Graph Grammars And Computing By Graph Transformation written by Grzegorz Rozenberg and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Computers categories.
Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others. The area of graph grammars and graph transformations generalizes formal language theory based on strings and the theory of term rewriting based on trees. As a matter of fact within the area of graph grammars, graph transformation is considered a fundamental programming paradigm where computation includes specification, programming, and implementation.
Handbook Of Graph Grammars And Computing By Graph Transformation Vol 1 Foundations
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Author : Grzegorz Rozenberg
language : en
Publisher: World Scientific
Release Date : 1997-02-27
Handbook Of Graph Grammars And Computing By Graph Transformation Vol 1 Foundations written by Grzegorz Rozenberg and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-02-27 with Computers categories.
Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others.The area of graph grammars and graph transformations generalizes formal language theory based on strings and the theory of term rewriting based on trees. As a matter of fact within the area of graph grammars, graph transformation is considered a fundamental programming paradigm where computation includes specification, programming, and implementation.Over the last 25-odd years graph grammars have developed at a steady pace into a theoretically attractive and well-motivated research field. In particular, they are now based on very solid foundations, which are presented in this volume. Volume 1 of the indispensable Handbook of Graph Grammars and Computing by Graph Transformations includes a state-of-the-art presentation of the foundations of all the basic approaches to rule-based graph specification and transformation: algebraic approach, logic approach, node-based rewriting, (hyper)edge-based rewriting, programmed graph rewriting, and 2-structures. The book has been written in a tutorial/survey style to enhance its usefulness.
Handbook Of Formal Languages
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Author : Grzegorz Rozenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 1997
Handbook Of Formal Languages written by Grzegorz Rozenberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Computers categories.
This third volume of the Handbook of Formal Languages discusses language theory beyond linear or string models: trees, graphs, grids, pictures, computer graphics. Many chapters offer an authoritative self-contained exposition of an entire area. Special emphasis is on interconnections with logic.
Foundations
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Author : Grzegorz Rozenberg
language : en
Publisher: World Scientific
Release Date : 1997
Foundations written by Grzegorz Rozenberg and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Graph grammars categories.
Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others.The area of graph grammars and graph transformations generalizes formal language theory based on strings and the theory of term rewriting based on trees. As a matter of fact within the area of graph grammars, graph transformation is considered a fundamental programming paradigm where computation includes specification, programming, and implementation.Over the last 25-odd years graph grammars have developed at a steady pace into a theoretically attractive and well-motivated research field. In particular, they are now based on very solid foundations, which are presented in this volume. Volume 1 of the indispensable Handbook of Graph Grammars and Computing by Graph Transformations includes a state-of-the-art presentation of the foundations of all the basic approaches to rule-based graph specification and transformation: algebraic approach, logic approach, node-based rewriting, (hyper)edge-based rewriting, programmed graph rewriting, and 2-structures. The book has been written in a tutorial/survey style to enhance its usefulness.
Graph Polynomials
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Author : Yongtang Shi
language : en
Publisher: CRC Press
Release Date : 2016-11-25
Graph Polynomials written by Yongtang Shi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-25 with Mathematics categories.
This book covers both theoretical and practical results for graph polynomials. Graph polynomials have been developed for measuring combinatorial graph invariants and for characterizing graphs. Various problems in pure and applied graph theory or discrete mathematics can be treated and solved efficiently by using graph polynomials. Graph polynomials have been proven useful areas such as discrete mathematics, engineering, information sciences, mathematical chemistry and related disciplines.