PARALLEL RECOGNITION OF HIGH DIMENSIONAL IMAGES

1992 ◽  
Vol 06 (02n03) ◽  
pp. 285-291 ◽  
Author(s):  
M. NIVAT ◽  
A. SAOUDI
Keyword(s):  
Time Complexity ◽  
Random Access ◽  
Space Complexity ◽  
Recognition Problem ◽  
High Dimensional ◽  
Context Free Grammar ◽  
Random Access Machine ◽  
Parallel Random Access Machine ◽  
Context Free ◽  
Context Free Grammars

We investigate the complexity of the recognition of images generated by a class of context-free image grammars. We show that the sequential time complexity of the recognition of an n × n image as generated by a context-free grammar is O(nM(n)), where M(n) is the time to multiply two boolean n × n matrices. The space complexity of this recognition is O(n3). Using a parallel random access machine (i.e. PRAM), the recognition can be done in O( log 2(n)) time with n7 processors or in O(n log 2(n)) time with n6 processors. We also introduce high dimensional context-free grammars and prove that their recognition problem is polylogarithmic.

scholarly journals Synchronous Context-Free Grammars and Optimal Parsing Strategies

2016 ◽  
Vol 42 (2) ◽  
pp. 207-243
Author(s):  
Daniel Gildea ◽  
Giorgio Satta
Keyword(s):  
Approximation Algorithms ◽  
Time Complexity ◽  
Space Complexity ◽  
Sentence Length ◽  
Np Hard ◽  
Space And Time ◽  
Context Free ◽  
General Graphs ◽  
Context Free Grammars

The complexity of parsing with synchronous context-free grammars is polynomial in the sentence length for a fixed grammar, but the degree of the polynomial depends on the grammar. Specifically, the degree depends on the length of rules, the permutations represented by the rules, and the parsing strategy adopted to decompose the recognition of a rule into smaller steps. We address the problem of finding the best parsing strategy for a rule, in terms of space and time complexity. We show that it is NP-hard to find the binary strategy with the lowest space complexity. We also show that any algorithm for finding the strategy with the lowest time complexity would imply improved approximation algorithms for finding the treewidth of general graphs.

Transforming comparison model lower bounds to the parallel-random-access-machine

1997 ◽  
Vol 62 (2) ◽  
pp. 103-110 ◽  
Author(s):  
Dany Breslauer ◽  
Artur Czumaj ◽  
Devdatt P. Dubhashi ◽  
Friedhelm Meyer auf der Heide
Keyword(s):  
Lower Bounds ◽  
Random Access ◽  
Comparison Model ◽  
Random Access Machine ◽  
Parallel Random Access Machine

scholarly journals Static Watson-Crick Context-Free Grammars

2019 ◽  
Vol 15 (10) ◽  
pp. 65 ◽  
Author(s):  
Wan Heng Fong ◽  
Aqilahfarhana Abdul Rahman ◽  
Nor Haniza Sarmin ◽  
Sherzod Turaev
Keyword(s):  
Dna Computing ◽  
Biological Properties ◽  
Dna Molecules ◽  
Context Free Grammar ◽  
Double Stranded Dna ◽  
New Variant ◽  
Sticker System ◽  
Relationship Of ◽  
Context Free ◽  
Context Free Grammars

Sticker systems and Watson-Crick automata are two modellings of DNA molecules in DNA computing. A sticker system is a computational model which is coded with single and double-stranded DNA molecules; while Watson-Crick automata is the automata counterpart of sticker system which represents the biological properties of DNA. Both of these models use the feature of Watson-Crick complementarity in DNA computing. Previously, the grammar counterpart of the Watson-Crick automata have been introduced, known as Watson-Crick grammars which are classified into three classes: Watson-Crick regular grammars, Watson-Crick linear grammars and Watson-Crick context-free grammars. In this research, a new variant of Watson-Crick grammar called a static Watson-Crick context-free grammar, which is a grammar counterpart of sticker systems that generates the double-stranded strings and uses rule as in context-free grammar, is introduced. The static Watson-Crick context-free grammar differs from a dynamic Watson-Crick context-free grammar in generating double-stranded strings, as well as for regular and linear grammars. The main result of the paper is to determine the generative powers of static Watson-Crick context-free grammars. Besides, the relationship of the families of languages generated by Chomsky grammars, sticker systems and Watson-Crick grammars are presented in terms of their hierarchy.

A REGULARITY CONDITION FOR CONTEXT-FREE GRAMMARS

2008 ◽  
Vol 19 (04) ◽  
pp. 845-857
Author(s):  
BEATRICE PALANO
Keyword(s):  
Lower Bound ◽  
Regularity Condition ◽  
Complexity Measure ◽  
Context Free Grammar ◽  
Context Free ◽  
Context Free Grammars

We define a complexity measure on context-free grammars called end. Roughly speaking, for a context-free grammar G, endG(n) measures the distance of variables from the ends of sentential forms along the derivations of words in L(G) of length n. We prove in a constructive way the regularity of L(G)wheneverendG(n)is constant. Yet, we improve on this by showing that ifL(G)is nonregular thenendG(n) = Ω∞( log n). We establish the optimality of such bound. Finally, we show that, in case of unambiguous context-free grammars, the end lower bound for generating nonregular languages turns out to be linear.

FUNCTIONAL PEARL Functional chart parsing of context-free grammars

2004 ◽  
Vol 14 (6) ◽  
pp. 669-680
Author(s):  
PETER LJUNGLÖF
Keyword(s):  
Data Structure ◽  
Time Complexity ◽  
Inference Rules ◽  
Global State ◽  
Bottom Up ◽  
Space And Time ◽  
Chart Parsing ◽  
The Many ◽  
Context Free ◽  
Context Free Grammars

This paper implements a simple and elegant version of bottom-up Kilbury chart parsing (Kilbury, 1985; Wirén, 1992). This is one of the many chart parsing variants, which are all based on the data structure of charts. The chart parsing process uses inference rules to add new edges to the chart, and parsing is complete when no further edges can be added. One novel aspect of this implementation is that it doesn't have to rely on a global state for the implementation of the chart. This makes the code clean, elegant and declarative, while still having the same space and time complexity as the standard imperative implementations.

scholarly journals The formal derivative operator and multifactorial numbers

2019 ◽  
Vol 53 (2) ◽  
pp. 125-137
Author(s):  
Juan Triana ◽  
Rodrigo De Castro
Keyword(s):  
Derivative Operator ◽  
Context Free Grammar ◽  
Context Free ◽  
Context Free Grammars

In this paper some properties, examples and counterexamples about the formal derivative operator defined with respect to context-free grammars are presented. In addition, we show a connection between the context-free grammar G = { a → abr; b → br+1 } and multifactorial numbers. Some identities involving multifactorial numbers will be obtained by grammatical methods.

scholarly journals Tunnel Parsing with counted repetitions

2020 ◽  
Vol 21 (4) ◽  
Author(s):  
Nikolay Handzhiyski ◽  
Elena Somova
Keyword(s):  
Efficient Algorithm ◽  
Time Complexity ◽  
Linear Time ◽  
Domain Specific Languages ◽  
Context Free Grammar ◽  
Syntax Tree ◽  
Domain Specific ◽  
Concrete Syntax ◽  
Parsing Algorithm ◽  
Context Free

The article describes a new and efficient algorithm for parsing, called Tunnel Parsing, that parses from left to right on the basis of a context-free grammar without left recursion and rules that recognize empty words. The algorithm is applicable mostly for domain-specific languages. In the article, particular attention is paid to the parsing of grammar element repetitions. As a result of the parsing, a statically typed concrete syntax tree is built from top to bottom, that accurately reflects the grammar. The parsing is not done through a recursion, but through an iteration. The Tunnel Parsing algorithm uses the grammars directly without a prior refactoring and is with a linear time complexity for deterministic context-free grammars.

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