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Context-free languages, groups, the theory of ends, second-order logic, tiling problems, cellular automata, and vector addition systems

David E. Muller, Paul E. Schupp
1981 Bulletin of the American Mathematical Society  
Using the results obtained and Rabin's theorem on the decidability of the monadic second-order theory of the infinite binary tree, we show that the monadic theory of any context-free graph is decidable  ...  We show that these problems all make sense on a very general class of graphs and are all solvable on any context-free graph.  ...  Using the results obtained and Rabin's theorem on the decidability of the monadic second-order theory of the infinite binary tree, we show that the monadic theory of any context-free graph is decidable  ... 
doi:10.1090/s0273-0979-1981-14904-1 fatcat:42es5b36onh2jjkrumryimhvri

Page 1155 of Mathematical Reviews Vol. , Issue 98B [page]

1998 Mathematical Reviews  
The algorithm applies to a class of language sampling problems that includes slices of context- free languages as a proper subclass.  ...  variants of the problem in this context.”  ... 

Page 2960 of Mathematical Reviews Vol. , Issue 95e [page]

1995 Mathematical Reviews  
William Gasarch (1-MD-C; College Park, MD) 95e:68171 68R10 68Q50 Wanke, Egon (D-PDRB-C; Paderborn) On the decidability of certain integer subgraph problems on context-free graph languages.  ...  As a consequence, we obtain the decidability of several subgraph prob- lems for graphs formed by a context-free hyperedge-replacement system.  ... 

Page 6542 of Mathematical Reviews Vol. , Issue 2000i [page]

2000 Mathematical Reviews  
In CFT routing, one reduces the number of “faults” that a routing problem has to deal with by using subgraphs to cover the faulty nodes.  ...  In particular, one considers the number and size (diameter) of faulty subgraphs rather than the number of faulty nodes that a graph can tolerate.  ... 

The bounded tree-width problem of context-free graph languages [chapter]

R. Skodinis
1997 Lecture Notes in Computer Science  
and 2. is the graph language generated by a given con uent NCE graph grammar an HR language? This settles the complexity of these important problems on graph grammars.  ...  We show that the following (equivalent) problems are Pcomplete: 1. Does a given con uent NCE graph grammar only generate graphs of bounded tree-width?  ...  It is known that it is decidable Cou95]. We show that it is P-complete. The proof is based on a pumping argument as it is known e.g. for the context-free string languages.  ... 
doi:10.1007/bfb0024506 fatcat:2j5psjojt5etbhlj4u2cbkpliq

The theory of ends, pushdown automata, and second-order logic

David E. Muller, Paul E. Schupp
1985 Theoretical Computer Science  
A class of edge-labeled graphs called context-free are defined according to their behavior at infinity. Such graphs are generalizations of Cayley graphs of context-free groups.  ...  Using Rabin's theorem on the monadic second-order theory of the infinite binary tree, these graphs are also shown to have a decidable monadic second-order theory.  ...  theory of any context-free graph is decidable.  ... 
doi:10.1016/0304-3975(85)90087-8 fatcat:tcgc5nkyqzb6lcv3mxmnhp52cm


David Fernández-Baca
2014 Algorithmica  
The conference covered a broad range of topics in theoretical computer science, including algorithms, automata theory and formal languages, coding theory and data compression, combinatorics and graph theory  ...  This special issue contains the journal versions of a selection of papers from the 10th Latin American Symposium on Theoretical Informatics (LATIN), held April 16-20, 2012 on the campus of Universidad  ...  The 2-disjoint connected subgraphs problem asks if there exist two vertex-disjoint connected subgraphs, such that each subgraph contains only one of the two sets of terminals.  ... 
doi:10.1007/s00453-014-9900-x fatcat:q4pscfbejzcvxaxpze3ufrkiau

Graph Structure and Monadic Second-Order Logic: Language Theoretical Aspects [chapter]

Bruno Courcelle
2008 Lecture Notes in Computer Science  
tools for the construction of Fixed-Parameter Tractable algorithms and also for the extension of methods and results of Formal Language Theory to the description of sets of finite graphs.  ...  Graph structure is a flexible concept covering many different types of graph properties.  ...  Walukiewicz for many useful comments on a first draft of this overview. The first 11 references are books and survey articles.  ... 
doi:10.1007/978-3-540-70575-8_1 fatcat:ftpcqszcb5fs5nswbqnbnmy5ja

Page 4078 of Mathematical Reviews Vol. , Issue 80J [page]

1980 Mathematical Reviews  
Such an algorithm does not exist for the class of all languages (I, P,~) where I has at least two elements and 9 is context-free.  ...  The subgraph homeomorphism problem. Conference Record of the Tenth Annual ACM Symposium on Theory of Computing (San Diego, Calif., 1978), pp. 40-50, ACM, New York, 1978.  ... 

Page 2056 of Mathematical Reviews Vol. , Issue 2003C [page]

2003 Mathematical Reviews  
Lower bounds are obtained on the degree and the number of monomials of polynomials over Zy,, which strongly or one-sidedly M-represent the Boolean function deciding whether a given n-bit integer is square-free  ...  Summary: “We give a complete characterization of parameter graphs H for which the problem of coloring H-free graphs is polynomial and for which it is NP-complete.  ... 

Combinatorial properties of boundary NLC graph languages

Grzegorz Rozenberg, Emo Welzl
1987 Discrete Applied Mathematics  
Hence, on the one hand one can view BNLC grammars as an analogue (in the framework of NLC grammars) of fundamental subfamilies of context-free string grammars (such as linear grammars or context-free grammars  ...  Although the membership problem for NLC grammars is decidable, NLC grammars can generate PSPACE-complete graph languages.  ...  Research of the second author has been partially supported by the Austrian "Fonds zur FSrderung der wissenschaftlichen Forschung" Combinatorial properties of boundary NLC graph languages  ... 
doi:10.1016/0166-218x(87)90054-0 fatcat:co23udgaxfdu3f6rvmce6wjzay

Page 6577 of Mathematical Reviews Vol. , Issue 97K [page]

1997 Mathematical Reviews  
Ginsburg [The mathematical theory of context-free languages, McGraw-Hill, New York, 1966; MR 35 #2692]. {For the entire collection see MR 97d:68007. } Leonid P.  ...  sense, for which the halting problem is decidable.  ... 

On Low Tree-Depth Decompositions [article]

Jaroslav Nesetril
2014 arXiv   pre-print
The theory of sparse structures usually uses tree like structures as building blocks. In the context of sparse/dense dichotomy this role is played by graphs with bounded tree depth.  ...  In more technical terms we survey some of the properties and applications of low tree depth decomposition of graphs.  ...  For every integers s and k, there is a polynomial time algorithm to decide whether a P s -free graph G is k-choosable. Proof. Assume G is P s -free.  ... 
arXiv:1412.1581v1 fatcat:pqx6dojaxbevlbl5pr7v3tl55u

The bounded degree problem for NLC grammars is decidable

Dirk Janssens, Grzegorz Rozenberg, Emo Welzl
1986 Journal of computer and system sciences (Print)  
Moreover, it is shown that, given an arbitrary NLC grammar G generating the language L(G) of bounded degree, one can effectively compute the maximum integer which appears as the degree of a graph in L(  ...  We demonstrate that it is decidable whether or not the (graph) language of an arbitrary node label controlled (NLC) grammar is of bounded degree.  ...  The problem can be stated as follows: "Given an NLC grammar G, is it decidable whether or not there is an integer n such that the degree of any node in any graph in the language, L(G), generated by G does  ... 
doi:10.1016/0022-0000(86)90060-7 fatcat:mgmhma2u2zadrc2goao3hrszom

Testing first-order properties for subclasses of sparse graphs

Zdeněk Dvořák, Daniel Král, Robin Thomas
2013 Journal of the ACM  
All our results also hold for relational structures and are based on the seminal result of Nešetřil and Ossona de Mendez on the existence of low tree-depth colorings.  ...  degree, graphs with no subgraph isomorphic to a subdivision of a fixed graph, and graphs that can be drawn in a fixed surface in such a way that each edge crosses at most a constant number of other edges  ...  A to decide the existence of an r-subdivision of the complete graph K m in an input graph from G, where the problem is parameterized by m.  ... 
doi:10.1145/2499483 fatcat:xpwop2si3vgmbkqzw6eoxlwsbu
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