MDL-BASED CONTEXT-FREE GRAPH GRAMMAR INDUCTION AND APPLICATIONS

2004 ◽  
Vol 13 (01) ◽  
pp. 65-79 ◽  
Author(s):  
ISTVAN JONYER ◽  
LAWRENCE B. HOLDER ◽  
DIANE J. COOK
Keyword(s):  
Real World ◽  
Graph Grammar ◽  
Graph Grammars ◽  
Grammar Induction ◽  
Free Graph ◽  
Context Free

We present an algorithm for the inference of context-free graph grammars from examples. The algorithm builds on an earlier system for frequent substructure discovery, and is biased toward grammars that minimize description length. Grammar features include recursion, variables and relationships. We present an illustrative example, demonstrate the algorithm's ability to learn in the presence of noise, and show real-world examples.

scholarly journals Context-free graph grammars

1978 ◽  
Vol 37 (2) ◽  
pp. 207-233 ◽  
Author(s):  
Pierluigi Della Vigna ◽  
Carlo Ghezzi
Keyword(s):  
Graph Grammars ◽  
Free Graph ◽  
Context Free

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

Context-free graph grammars and concatenation of graphs

1997 ◽  
Vol 34 (10) ◽  
pp. 773-803 ◽  
Author(s):  
Joost Engelfriet ◽  
Jan Joris Vereijken
Keyword(s):  
Graph Grammars ◽  
Free Graph ◽  
Context Free

scholarly journals Graphs and Decidable Transductions based on Edge Constraints

1994 ◽  
Vol 1 (4) ◽  
Author(s):  
Nils Klarlund ◽  
Michael I. Schwartzbach
Keyword(s):  
Spanning Trees ◽  
Second Order ◽  
Order Logic ◽  
Graph Grammar ◽  
Hoare Logic ◽  
Free Graph ◽  
Graph Families ◽  
Context Free ◽  
Second Order Logic ◽  
Monadic Second Order Logic

We give examples to show that not even <strong> c-edNCE</strong>, the most general known notion of context-free graph grammar, is suited for the specification of some common data structures.<br /> <br />To overcome this problem, we use monadic second-order logic and introduce <em> edge constraints</em> as a new means of specifying a large class of graph families. Our notion stems from a natural dichotomy found in programming practice between ordinary pointers forming spanning trees and auxiliary pointers cutting across.<br /> <br />Our main result is that for certain transformations of graphs definable in monadic second-order logic, the question of whether a graph family given by a specification A is mapped to a family given by a specification B is decidable. Thus a decidable Hoare logic arises.

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