Context-free languages, their two-dimensional generalisation, related tasks

2002 ◽  
pp. 479-505
Author(s):  
Michail I. Schlesinger ◽  
Václav Hlaváč
Keyword(s):  
Two Dimensional ◽  
Context Free

CONTEXT-SENSITIVITY OF TWO-DIMENSIONAL REGULAR ARRAY GRAMMARS

1989 ◽  
Vol 03 (03n04) ◽  
pp. 295-319 ◽  
Author(s):  
YASUNORI YAMAMOTO ◽  
KENICHI MORITA ◽  
KAZUHIRO SUGATA
Keyword(s):  
Context Sensitivity ◽  
The Other ◽  
Two Dimensional ◽  
Regular Array ◽  
Nonterminal Symbol ◽  
Left Hand ◽  
Other Hand ◽  
Context Free ◽  
Rewriting Rules

Regular array grammars (RAGs) are the lowest subclass in the Chomsky-like hierarchy of isometric array grammars. The left-hand side of each rewriting rule of RAGs has one nonterminal symbol and at most one "#" (a blank symbol). Therefore, the rewriting rules cannot sense contexts of non-# symbols. However, they can sense # as a kind of context. In this paper, we investigate this #-sensing ability. and study the language generating power of RAGs. Making good use of this ability, We show a method for RAGs to sense the contexts of local shapes of a host array in a derivation. Using this method, we give RAGs which generate the sets of all solid upright rectangles and all solid squares. On the other hand. it is proved that there is no context-free array grammar (and thus no RAG) which generates the set of all hollow upright rectangles.

Expressiveness and complexity of regular pure two-dimensional context-free languages

2013 ◽  
Vol 90 (8) ◽  
pp. 1708-1733 ◽  
Author(s):  
Marcello M. Bersani ◽  
Achille Frigeri ◽  
Alessandra Cherubini
Keyword(s):  
Two Dimensional ◽  
Context Free

PUSHDOWN RECOGNIZERS FOR ARRAY PATTERN

1989 ◽  
Vol 03 (03n04) ◽  
pp. 377-392
Author(s):  
H. J. LIN ◽  
P. S. P. WANG
Keyword(s):  
Two Dimensional ◽  
One Dimensional ◽  
Array Pattern ◽  
The Relationship ◽  
Context Free ◽  
Pushdown Automata

We investigate the factors that make it difficult to generalize pushdown automata for one-dimensional strings to two-dimensional arrays. Then we resolve the problems and construct two-dimensional pushdown array automata (PDAA). The relationship between isometric context-free array languages and pushdown array automata is established. Several examples of array automata are presented, and a pushdown array automaton is tested on VAX8650/VMS using PASCAL.

GENERATING RECTANGLES USING TWO-DIMENSIONAL GRAMMARS WITH TIME AND SPACE COMPLEXITY ANALYSES

1989 ◽  
Vol 03 (03n04) ◽  
pp. 321-332 ◽  
Author(s):  
EDWARD T. LEE ◽  
SHANG-YONG ZHU ◽  
PENG-CHING CHU
Keyword(s):  
Pattern Recognition ◽  
Information System ◽  
Space Complexity ◽  
Two Dimensional ◽  
Time And Space ◽  
Information System Design ◽  
Filling Pattern ◽  
Time And Space Complexity ◽  
Context Free ◽  
Region Filling

A two-dimensional grammar for generating all possible rectangles is presented and illustrated by examples. The time and space complexity analyses of this grammar together with a parallel context-free array grammar and a free grammar are also presented. Generating pictures using two-dimensional grammars appear to be a fertile field for further study. The study of two-dimensional grammars has useful applications in region filling. pattern recognition. robotics, pictorial information system design and related areas.

RECURRENT TWO-DIMENSIONAL SEQUENCES GENERATED BY HOMOMORPHISMS OF FINITE ABELIAN p-GROUPS WITH PERIODIC INITIAL CONDITIONS

Fractals ◽  
2011 ◽  
Vol 19 (04) ◽  
pp. 431-442 ◽  
Author(s):  
MIHAI PRUNESCU
Keyword(s):  
Initial Conditions ◽  
Two Dimensional ◽  
Pascal’S Triangle ◽  
Modulo P ◽  
Pascal's Triangle ◽  
Context Free

We prove that if a recurrent two-dimensional sequence with periodic initial conditions coincides in a sufficiently large starting square with a two-dimensional sequence produced by an expansive system of context-free substitutions, then they must coincide everywhere. We apply this result for some examples built up by homomorphisms of finite abelian p-groups, in particular for Pascal's Triangle modulo pk, Pascal's Triangles modulo 2 with non-trivial periodic borders, and Sierpinski's Carpets with non-trivial periodic border. All these particular cases justify the conjecture that recurrent two-dimensional sequences generated by homomorphisms of finite abelian p-groups with periodic initial conditions can always be alternatively generated by expansive systems of context-free substitutions.

Spectrophotometric measurements of objective-prism spectra

1966 ◽  
Vol 24 ◽  
pp. 118-119
Author(s):  
Th. Schmidt-Kaler
Keyword(s):  
Progress Report ◽  
Two Dimensional ◽  
Objective Prism ◽  
Made In

I should like to give you a very condensed progress report on some spectrophotometric measurements of objective-prism spectra made in collaboration with H. Leicher at Bonn. The procedure used is almost completely automatic. The measurements are made with the help of a semi-automatic fully digitized registering microphotometer constructed by Hög-Hamburg. The reductions are carried out with the aid of a number of interconnected programmes written for the computer IBM 7090, beginning with the output of the photometer in the form of punched cards and ending with the printing-out of the final two-dimensional classifications.

Sign in / Sign up

Export Citation Format

Share Document