Context-Free Graph Grammars

Graph languages are sets of labeled graphs. They can be generated by graph grammars, and in particular by context-free graph grammars. There are several types of context-free graph grammars, depending, e.g., on whether (hyper)edges or nodes are rewritten by graphs. Basic properties of the main types of context-free graph grammars are discussed. Other, equivalent, ways of defining context-free graph languages are: generating graph expressions by regular tree grammars, and translating trees into graphs by formulas of monadic second-order logic. Context-free graph grammars can be used to generate string languages and tree languages.

[1]  Jesse B. Wright,et al.  Algebraic Automata and Context-Free Sets , 1967, Inf. Control..

[2]  Bruno Courcelle,et al.  The Obstructions of a Minor-Closed Set of Graphs Defined by Hyperedge Replacement can be Constructed , 1994, TAGT.

[3]  Thomas Lengauer,et al.  Efficient decision procedures for graph properties on context-free graph languages , 1993, JACM.

[4]  Joost Engelfriet,et al.  A Characterization of Context-Free NCE Graph Languages by Monadic Second-Order Logic on Trees , 1990, Graph-Grammars and Their Application to Computer Science.

[5]  John Doner,et al.  Tree Acceptors and Some of Their Applications , 1970, J. Comput. Syst. Sci..

[6]  Bruno Courcelle,et al.  A Logical Characterization of the Sets of Hypergraphs Defined by Hyperedge Replacement Grammars , 1995, Math. Syst. Theory.

[7]  Joost Engelfriet,et al.  Tree transducers, L systems and two-way machines (Extended Abstract) , 1978, J. Comput. Syst. Sci..

[8]  Jozef Gruska Generalized context-free grammars , 1973, Acta Cybern..

[9]  Clemens Lautemann,et al.  Decomposition Trees: Structured Graph Representation and Efficient Algorithms , 1988, CAAP.

[10]  J. Büchi Weak Second‐Order Arithmetic and Finite Automata , 1960 .

[11]  Mikkel Thorup,et al.  All Structured Programs have Small Tree-Width and Good Register Allocation , 1998, Inf. Comput..

[12]  Annegret Habel,et al.  May we introduce to you: hyperedge replacement , 1986, Graph-Grammars and Their Application to Computer Science.

[13]  Grzegorz Rozenberg,et al.  Graph Grammars with Neighbourhood-Controlled Embedding , 1982, Theor. Comput. Sci..

[14]  Derek G. Corneil,et al.  Complement reducible graphs , 1981, Discret. Appl. Math..

[15]  Joost Engelfriet,et al.  The Translation Power of Top-Down Tree-to-Graph Transducers , 1994, J. Comput. Syst. Sci..

[16]  C. C. Elgot Decision problems of finite automata design and related arithmetics , 1961 .

[17]  Bruno Courcelle,et al.  Graph Rewriting: An Algebraic and Logic Approach , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[18]  Bruno Courcelle,et al.  The Monadic Second-Order Logic of Graphs V: On Closing the Gap Between Definability and Recognizability , 1991, Theor. Comput. Sci..

[19]  Grzegorz Rozenberg,et al.  A Survey of NLC Grammars , 1983, CAAP.

[20]  Konstantin Skodinis,et al.  Graph Automata for Linear Graph Languages , 1994, TAGT.

[21]  Emo Welzl On the Set of all Subgraphs of the Graphs in a Boundary NLC Graph Language , 1986 .

[22]  Jean-Claude Raoult Recursively Defined Tree Transductions , 1993, RTA.

[23]  Renate Klempien-Hinrichs Node Replacement in Hypergrahps: Simulation of Hyperedge Replacement, and Decidability of Confluence , 1994, TAGT.

[24]  Franz-Josef Brandenburg,et al.  On Polynomial Time Graph Grammars , 1988, STACS.

[25]  David J. Weir Linear Context-Free Rewriting Systems and Deterministic Tree-Walking Transducers , 1992, ACL.

[26]  Annegret Habel Hypergraph Grammars: Transformational and Algorithmic Aspects , 1992, J. Inf. Process. Cybern..

[27]  Paul D. Seymour,et al.  Graph Minors. II. Algorithmic Aspects of Tree-Width , 1986, J. Algorithms.

[28]  Ton Kloks Treewidth, Computations and Approximations , 1994, Lecture Notes in Computer Science.

[29]  Franz-Josef Brandenburg The computational complexity of certain graph grammars , 1983 .

[30]  Annegret Habel,et al.  Decidable Boundedness Problems for Sets of Graphs Generated by Hyperedge-Replacement , 1991, Theor. Comput. Sci..

[31]  Grzegorz Rozenberg,et al.  Boundary NLC Graph Grammars-Basic Definitions, Normal Forms, and Complexity , 1986, Inf. Control..

[32]  Bruno Courcelle,et al.  Monadic Second-Order Definable Graph Transductions: A Survey , 1994, Theor. Comput. Sci..

[33]  Joost Englfriet The complexity of languages generated by attribute grammars , 1986 .

[34]  Annegret Habel,et al.  Characteristics of Graph Languages Generated by Edge Replacement , 1987, Theor. Comput. Sci..

[35]  Joost Engelfriet An Elementary Proof of Double Greibach Normal Form , 1992, Inf. Process. Lett..

[36]  Tadao Kasami,et al.  On Multiple Context-Free Grammars , 1991, Theor. Comput. Sci..

[37]  Joost Engelfriet,et al.  Hypergraph Languages of Bounded Degree , 1994, J. Comput. Syst. Sci..

[38]  Grzegorz Rozenberg,et al.  On the structure of node-label-controlled graph languages , 1980, Inf. Sci..

[39]  Joost Engelfriet,et al.  Context-free graph grammars and concatenation of graphs , 1997, Acta Informatica.

[40]  Walter Vogler On Hyperedge Replacement and BNLC Graph Grammars , 1993, Discret. Appl. Math..

[41]  David J. Weir,et al.  Characterizing Structural Descriptions Produced by Various Grammatical Formalisms , 1987, ACL.

[42]  Changwook Kim,et al.  HRNCE Grammars - A Hypergraph Generating System with an eNCE Way , 1994, TAGT.

[43]  Franz-Josef Brandenburg The Equivalence of Boundary and Confluent Graph Grammars on Graph Languages of Bounded Degree , 1991, RTA.

[44]  Annegret Habel,et al.  A Comparison of Compatible, Finite, and Inductive Graph Properties , 1993, Theor. Comput. Sci..

[45]  Bruno Courcelle Structural Properties of Context-Free Sets of Graphs Generated by Vertex Replacement , 1995, Inf. Comput..

[46]  Bruno Courcelle,et al.  Graph grammars, monadic second-order logic and the theory of graph minors , 1991, Graph Structure Theory.

[47]  S. Ginsburg,et al.  Finite-Turn Pushdown Automata , 1966 .

[48]  Bruno Courcelle,et al.  The Monadic Second-Order Logic of Graphs. I. Recognizable Sets of Finite Graphs , 1990, Inf. Comput..

[49]  Bruno Courcelle,et al.  Monadic Second-Order Evaluations on Tree-Decomposable Graphs , 1993, Theor. Comput. Sci..

[50]  Annegret Habel,et al.  Some Structural Aspects of Hypergraph Languages Generated by Hyperedge Replacement , 1987, STACS.

[51]  Hans L. Bodlaender,et al.  A Partial k-Arboretum of Graphs with Bounded Treewidth , 1998, Theor. Comput. Sci..

[52]  Grzegorz Rozenberg,et al.  Combinatorial properties of boundary NLC graph languages , 1987, Discret. Appl. Math..

[53]  Joost Engelfriet,et al.  A Greibach Normal Form for Context-free Graph Grammars , 1992, ICALP.

[54]  Hans-Jörg Kreowski,et al.  Five Facets of Hyperedge Replacement Beyond Context-Freeness , 1993, FCT.

[55]  Annegret Habel,et al.  Filtering Hyperedge-Replacement Through Compatible Properties , 1989, WG.

[56]  Egon Wanke,et al.  Emptiness Problems of eNCE Graph Languages , 1995, J. Comput. Syst. Sci..

[57]  Bruno Courcelle,et al.  Handle-Rewriting Hypergraph Grammars , 1993, J. Comput. Syst. Sci..

[58]  Emo Welzl,et al.  Encoding Graphs by Derivations and Implications for the Theory of Graph Grammars , 1984, ICALP.

[59]  Bruno Courcelle,et al.  The monadic second-order logic of graphs III: tree-decompositions, minor and complexity issues , 1992, RAIRO Theor. Informatics Appl..

[60]  Paul D. Seymour,et al.  Graph minors. I. Excluding a forest , 1983, J. Comb. Theory, Ser. B.

[61]  Jozef Gruska A Characterization of Context-free Languages , 1971, J. Comput. Syst. Sci..

[62]  Bruno Courcelle An Axiomatic Definition of Context-Free Rewriting and its Application to NLC Graph Grammars , 1987, Theor. Comput. Sci..

[63]  Ken Kennedy,et al.  Graph grammars and global program data flow analysis , 1976, 17th Annual Symposium on Foundations of Computer Science (sfcs 1976).

[64]  Bruno Courcelle,et al.  The Monadic Second-Order Logic of Graphs VII: Graphs as Relational Structures , 1992, Theor. Comput. Sci..

[65]  Bruno Courcelle,et al.  The Monadic Second order Logic of Graphs VI: on Several Representations of Graphs By Relational Structures , 1994, Discret. Appl. Math..

[66]  Bruno Courcelle,et al.  Basic Notions of Universal Algebra for Language Theory and Graph Grammars , 1996, Theor. Comput. Sci..

[67]  Joost Engelfriet,et al.  A Comparison of Boundary Graph Grammars and Context-Free Hypergraph Grammars , 1990, Inf. Comput..

[68]  Jean Berstel,et al.  Transductions and context-free languages , 1979, Teubner Studienbücher : Informatik.

[69]  Joost Engelfriet,et al.  Boundary Graph Grammars with Dynamic Edge Relabeling , 1990, J. Comput. Syst. Sci..

[70]  Sheila A. Greibach,et al.  One Way Finite Visit Automata , 1978, Theor. Comput. Sci..

[71]  Seymour Ginsburg,et al.  Derivation-Bounded Languages , 1968, J. Comput. Syst. Sci..

[72]  Joost Engelfriet,et al.  The String Generating Power of Context-Free Hypergraph Grammars , 1991, J. Comput. Syst. Sci..

[73]  Egon Wanke,et al.  Algorithms for Graph Problems on BNLC Structured Graphs , 1991, Inf. Comput..

[74]  Joost Engelfriet,et al.  Linear Graph Grammars: Power and Complexity , 1989, Inf. Comput..