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

1981
*
Bulletin of the American Mathematical Society
*

Using

doi:10.1090/s0273-0979-1981-14904-1
fatcat:42es5b36onh2jjkrumryimhvri
*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*...##
###
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]

1997
*
Lecture Notes in Computer Science
*

and 2. is

doi:10.1007/bfb0024506
fatcat:2j5psjojt5etbhlj4u2cbkpliq
*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*. ...##
###
The theory of ends, pushdown automata, and second-order logic

1985
*
Theoretical Computer Science
*

A class

doi:10.1016/0304-3975(85)90087-8
fatcat:tcgc5nkyqzb6lcv3mxmnhp52cm
*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*. ...##
###
Editorial

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. ...

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

2008
*
Lecture Notes in Computer Science
*

tools for

doi:10.1007/978-3-540-70575-8_1
fatcat:ftpcqszcb5fs5nswbqnbnmy5ja
*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. ...##
###
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

1987
*
Discrete Applied Mathematics
*

Hence,

doi:10.1016/0166-218x(87)90054-0
fatcat:co23udgaxfdu3f6rvmce6wjzay
*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*...##
###
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]

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*. ...

##
###
The bounded degree problem for NLC grammars is decidable

1986
*
Journal of computer and system sciences (Print)
*

Moreover, it is shown that, given an arbitrary NLC grammar G generating

doi:10.1016/0022-0000(86)90060-7
fatcat:mgmhma2u2zadrc2goao3hrszom
*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 ...##
###
Testing first-order properties for subclasses of sparse graphs

2013
*
Journal of the ACM
*

All our results also hold for relational structures and are based

doi:10.1145/2499483
fatcat:xpwop2si3vgmbkqzw6eoxlwsbu
*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. ...
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