scholarly journals Patterns, Graphs and DNA

1994 ◽  
Vol 23 (484) ◽  
Author(s):  
Brian H. Mayoh
Keyword(s):  
Expressive Power ◽  
Transfer Rna ◽  
Neural Nets ◽  
Graph Grammars ◽  
Dna And Rna ◽  
Virus Rna ◽  
Pattern Approach ◽  
Genetic Algorithm Approach ◽  
Dna Pattern ◽  
Context Free

Two papers in one! The first, ``On Patterns and Graphs´´, describes the pattern version of context-free grammars for many kinds of substitution structures. By giving striking examples, particularly for emotional neural nets and other forms of graph grammars, it shows that the extra expressive power of pattern multigrammars is worth having. The second paper, ``DNA pattern multigrammars´´ describes the pattern approach to the analysis of the secondary structure of DNA and RNA; in particular it gives an analysis of Tobacco Mosaic Virus RNA, Transfer RNA, and genetic switching in the bacteriophage l. The genetic algorithm approach to the machine learning of DNA and RNA grammars is also discussed.

scholarly journals A comparison of boundary graph grammars and context-free hypergraph grammars

1990 ◽  
Vol 84 (2) ◽  
pp. 163-206 ◽  
Author(s):  
Joost Engelfiet ◽  
Grzegorz Rozenberg
Keyword(s):  
Graph Grammars ◽  
Context Free ◽  
Boundary Graph

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

scholarly journals The binding of T4 gene 32 protein to MS2 virus RNA and transfer RNA

1980 ◽  
Vol 8 (6) ◽  
pp. 1357-1372 ◽  
Author(s):  
Pedro Suau ◽  
Jean-Jacques Toulmé ◽  
Claude Hélène
Keyword(s):  
Transfer Rna ◽  
Virus Rna ◽  
Gene 32 ◽  
T4 Gene 32 Protein

scholarly journals Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU Activations

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 992 ◽  
Author(s):  
Boris Hanin
Keyword(s):  
Convex Functions ◽  
Expressive Power ◽  
Scalar Function ◽  
Universal Function ◽  
Unit Cube ◽  
Neural Nets ◽  
Minimal Width ◽  
Continuous Convex Function ◽  
Dimensional Cube ◽  
Bounded Width

This article concerns the expressive power of depth in neural nets with ReLU activations and a bounded width. We are particularly interested in the following questions: What is the minimal width w min ( d ) so that ReLU nets of width w min ( d ) (and arbitrary depth) can approximate any continuous function on the unit cube [ 0 , 1 ] d arbitrarily well? For ReLU nets near this minimal width, what can one say about the depth necessary to approximate a given function? We obtain an essentially complete answer to these questions for convex functions. Our approach is based on the observation that, due to the convexity of the ReLU activation, ReLU nets are particularly well suited to represent convex functions. In particular, we prove that ReLU nets with width d + 1 can approximate any continuous convex function of d variables arbitrarily well. These results then give quantitative depth estimates for the rate of approximation of any continuous scalar function on the d-dimensional cube [ 0 , 1 ] d by ReLU nets with width d + 3 .

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 A Novel method to represent Access Tree structure by Context Free Grammar with and-or graph in Key Policy based Attribute based Encryption

2018 ◽  
Vol 7 (4.10) ◽  
pp. 396
Author(s):  
K. Senthil Kumar ◽  
D. Malathi
Keyword(s):  
Access Control ◽  
Control Structure ◽  
Expressive Power ◽  
Third Party ◽  
Efficient Manner ◽  
Context Free Grammar ◽  
Fine Grained ◽  
Attribute Based Encryption ◽  
Key Policy ◽  
Context Free

Important and sensitivity data of users in a third party managed internet or cloud always pose various security as well as privacy issues. Attribute-based encryption (ABE) is a pleasant trend in the literature which addresses above problem in an efficient way, and provides data security and fine-grained access control in a decentralized manner,. Key-policy attribute-based encryption (KP-ABE) is an important type of ABE, in which user can decrypt his message with a set of attributes and private keys are embedded with a access control structure which defines which cipher text  an user can be allowed to decrypt. In this paper we use a probabilistic context free grammar with an And-Or structure to represent access control structure. And-Or graph has high expressive power hence access control structure can be represented in an efficient manner.  

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