Decidable Boundedness Problems for Hyperedge-Replacement Graph Grammar

@inproceedings{Habel1989DecidableBP,
  title={Decidable Boundedness Problems for Hyperedge-Replacement Graph Grammar},
  author={Annegret Habel and Hans-J{\"o}rg Kreowski and Walter Vogler},
  booktitle={TAPSOFT, Vol.1},
  year={1989}
}
Consider a class C of hyperedge-replacement graph grammars and a numeric function on graphs like the number of edges, the degree (i.e., the maximum of the degrees of all nodes of a graph), the number of simple paths, the size of a maximum set of independent nodes, etc. Each such function induces a Boundedness Problem for the class C: Given a grammar HRG in C, are the function values of all graphs in the language L(HRG), generated by HRG, bounded by an integer or not? We show that the… 

On the Decidability of Integer Subgraph Problems on Context-Free Graph Languages

We show the decidability of integer subgraph problems (ISPs) on context-free sets of graphs L(Γ) defined by hyperedge replacement systems (HRSs) Γ. Additionally, we give a very general

On the Decidability of Certain Integer Subgraph Problems on Context-Free Graph Languages

  • Egon Wanke
  • Mathematics, Computer Science
    Inf. Comput.
  • 1994
Using integer linear programming methods, the decidability of certain integer subgraph problems (ISPs) on context-free sets of graphs L(Γ) defined by hyperedged replacement systems (HRSs)Γ is shown.

The complexity of graph languages generated by hyperedge replacement

The main difficulty in HRG parsing is analysed and some conditions on either grammar or input graphs are developed under which parsing can be done in polynomial time.

The Complexity of Connectivity Problems on Context-Free Graph Languages

  • Egon Wanke
  • Computer Science, Mathematics
    J. Comput. Syst. Sci.
  • 1994

Monadic Second-Order Evaluations on Tree-Decomposable Graphs

Five Facets of Hyperedge Replacement Beyond Context-Freeness

Hyperedge replacement is studied for more than twenty years as a rulebased device for the generation of sets of graphs, hypergraphs and other graphlike structures providing mainly a graph-grammatical counterpart to context-free Chomsky grammars.

Finite Tree Automata with Cost Functions

  • H. Seidl
  • Mathematics, Computer Science
    Theor. Comput. Sci.
  • 1992

A Characterization of Context-Free NCE Graph Languages by Monadic Second-Order Logic on Trees

  • J. Engelfriet
  • Computer Science
    Graph-Grammars and Their Application to Computer Science
  • 1990
A graph language L is in the class C-edNCE of context-free NCE graph languages if and only if L=f(T) where f is a function on graphs that can be defined in monadic second-order logic and T is the set

References

SHOWING 1-10 OF 14 REFERENCES

The Bounded Degree Problem for NLC Grammars is Decidable

Graph-Theoretic Properties Compatible with Graph Derivations

The concept of compatible properties is introduced, the compatibility of connectedness, existence of Eulerian paths and cycles, and edge-colorability are shown, and the decidability result is applied to these distinguished properties.

Efficient Analysis of Graph Properties on Context-free Graph Languages (Extended Abstract)

A characteristic called ”finiteness” of graph properties is defined and a combinatorial decision algorithm for deciding whether a graph language generated by a given cellular graph grammar has a graph with a given finite graph property is given.

A Pumping Lemma for Context-Free Graph Languages

  • H. Kreowski
  • Mathematics, Computer Science
    Graph-Grammars and Their Application to Computer Science and Biology
  • 1978
This generalization of the well-known pumping lemma for context-free Chomsky languages is formulated and proved, where the iteration of LINK in the chain gluing leads to the pumping effect.

Problems Easy for Tree-Decomposable Graphs (Extended Abstract)

It is shown that all graph properties definable in monadic second order logic (MS properties) with quantification over vertex and edge sets can be decided in linear time for classes of graphs of fixed bounded tree-width, giving an alternative proof of a recent result by Courcelle.

Some Structural Aspects of Hypergraph Languages Generated by Hyperedge Replacement

The concept combines a context-free type of rewriting with a comparatively large generative power for generating hypergraph languages including graph languages and string languages.

On context-free gragh languages generated by edge replacement

  • A. HabelH. Kreowski
  • Computer Science
    Graph-Grammars and Their Application to Computer Science
  • 1982
This paper summarizes some recent results on graph languages generated by edge replacement and shows that their languages are fixed points of their productions and that they can be generated by language operations from finite graph languages.

On context-free sets of graphs and their monadic second-order theory

  • B. Courcelle
  • Mathematics, Computer Science
    Graph-Grammars and Their Application to Computer Science
  • 1986
Context-free graph grammars (where the rewriting step is the substitution a graph for an hyperedge) are defined and the monadic second-order theory of a context-free set of graphs is decidable.