The bounded tree-width problem of context-free graph languages

1997 ◽  
pp. 303-317
Author(s):  
R. Skodinis
Keyword(s):  
Free Graph ◽  
Tree Width ◽  
Context Free ◽  
Graph Languages

On spectra of sentences of monadic second order logic with counting

2004 ◽  
Vol 69 (3) ◽  
pp. 617-640 ◽  
Author(s):  
E. Fischer ◽  
J. A. Makowsky
Keyword(s):  
Second Order ◽  
Order Logic ◽  
Graph Grammars ◽  
Free Graph ◽  
Unary Relation ◽  
Tree Width ◽  
Binary Relation Symbol ◽  
Context Free ◽  
Second Order Logic ◽  
Monadic Second Order Logic

Abstract.We show that the spectrum of a sentence ϕ in Counting Monadic Second Order Logic (CMSOL) using one binary relation symbol and finitely many unary relation symbols, is ultimately periodic, provided all the models of ϕ are of clique width at most k, for some fixed k. We prove a similar statement for arbitrary finite relational vocabularies τ and a variant of clique width for τ-structures. This includes the cases where the models of ϕ are of tree width at most k. For the case of bounded tree-width, the ultimate periodicity is even proved for Guarded Second Order Logic GSOL. We also generalize this result to many-sorted spectra, which can be viewed as an analogue of Parikh's Theorem on context-free languages, and its analogues for context-free graph grammars due to Habel and Courcelle.Our work was inspired by Gurevich and Shelah (2003), who showed ultimate periodicity of the spectrum for sentences of Monadic Second Order Logic where only finitely many unary predicates and one unary function are allowed. This restriction implies that the models are all of tree width at most 2, and hence it follows from our result.

Context-free graph languages of bounded degree are generated by apex graph grammars

1994 ◽  
Vol 31 (4) ◽  
pp. 341-378 ◽  
Author(s):  
Joost Engelfriet ◽  
Linda Heyker ◽  
George Leih
Keyword(s):  
Graph Grammars ◽  
Free Graph ◽  
Bounded Degree ◽  
Apex Graph ◽  
Context Free ◽  
Graph Languages

scholarly journals Logical Description of Context-free Graph Languages

1997 ◽  
Vol 55 (3) ◽  
pp. 489-503 ◽  
Author(s):  
Joost Engelfriet ◽  
Vincent van Oostrom
Keyword(s):  
Free Graph ◽  
Logical Description ◽  
Context Free ◽  
Graph Languages

scholarly journals Regular Description of Context-free Graph Languages

1996 ◽  
Vol 53 (3) ◽  
pp. 556-574 ◽  
Author(s):  
Joost Engelfriet ◽  
Vincent van Oostrom
Keyword(s):  
Free Graph ◽  
Context Free ◽  
Graph Languages
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