Book Chapter10.1007/BFB0017410
Tree Automata, Tree Decomposition and Hyperedge Replacement
Clemens Lautemann
- 05 Mar 1990
- pp 520-537
10
TL;DR: Recent results concerning efficient solvability of graph problems on graphs with bounded tree-width and decidability ofGraph properties for hyperedge-replacement graph grammars are systematised by showing how they can be derived from recognisability of corresponding tree classes by finite tree automata using only well-known techniques from tree-automata theory.
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Abstract: Recent results concerning efficient solvability of graph problems on graphs with bounded tree-width and decidability of graph properties for hyperedge-replacement graph grammars are systematised by showing how they can be derived from recognisability of corresponding tree classes by finite tree automata, using only well-known techniques from tree-automata theory.
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Citations
•Book
Hyperedge replacement graph grammars
Frank Drewes,Hans-Jörg Kreowski,Annegret Habel +2 more
- 01 Feb 1997
TL;DR: To cover a large part of the theory of hyperedge replacement, structural properties and decision problems, including the membership problem, are addressed.
303
Hyperedge replacement graph grammars
Frank Drewes,Hans‐Jörg Kreowski,Annegret Habel +2 more
- 01 Feb 1997
TL;DR: The paper presents hyperedge replacement graph grammars as a graph-grammatical counterpart to context-free string grammars. The paper covers structural properties and decision problems, including the membership problem.
247
Context-free graph languages of bounded degree are generated by apex graph grammars
TL;DR: The apex graph grammars generate precisely the context-free graph languages of bounded degree, independently of whether one considers hyperedge replacement systems or (boundary or confluent) NLC or edNCE graph Grammars.
22
Treewidth, pathwidth and cospan decompositions with applications to graph-accepting tree automata
TL;DR: This work will revisit the categorical notion of cospan decompositions of graphs and compare it to the well-known notions of path decomposition and tree decomposition from graph theory, and show that regardless of whether the authors consider path or tree decomposition, they arrive at the same notion of recognizability.
17
Treewidth, Pathwidth and Cospan Decompositions
TL;DR: Several types of cospan decompositions with appropriate width measures are defined and it is shown that these width measures coincide with pathwidth and treewidth.
10
References
•Book
Introduction to Automata Theory, Languages, and Computation
John E. Hopcroft,Rajeev Motwani,Rotwani,Jeffrey D. Ullman +3 more
- 01 Jan 1979
TL;DR: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity, appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.
14.5K
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The NP-completeness column: An ongoing guide
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