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Contextual Array Grammars with Matrix and Regular Control
[chapter]
2016
Lecture Notes in Computer Science
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For d ≥ 2, d-dimensional contextual array grammars are less powerful than matrix contextual array grammars, which themselves are less powerful than contextual array grammars with regular control languages ...
We investigate the computational power of d-dimensional contextual array grammars with matrix control and regular control languages. ...
On the other hand, in the 1-dimensional case, the following theorem says that even with the regulating mechanisms of matrix control or regular control languages, with 1-dimensional contextual array grammars ...
doi:10.1007/978-3-319-41114-9_8
fatcat:2kyzz6kqrzb75pidwu6opbj43a
Sequential/Parallel Matrix Array Languages
1975
Journal of Cybernetics
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Cool A new system called sequential/parallel matrix grammars for two-dimensional pattern processing is introduced and studied. ...
We also give regular-like expressions and array grammars that describe sets of matrices or rectangular arrays with fixed proportions. Finally, several related future research topics are mentioned. ...
For instance,a triangle
X
can be represented by a 2-dimensional array
AC
AIC
YBBZ
constructed an
appropriate mathematical model of 2-dimensional pattern grammars
on the set of 2-dimensional ...
doi:10.1080/01969727508545918
fatcat:yp6d5q4eozd6hcackbh6ba7hhi
Page 4575 of Mathematical Reviews Vol. , Issue 98G
[page]
1998
Mathematical Reviews
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For example, for each recursively enumerable string language L there exists a quasi-monotonic one-dimensional array grammar generating the array image of L.” ...
Summary: “As in the string case, for n-dimensional array gram- mars we obtain regular, context-free, and monotonic grammars by imposing specific restrictions on the corresponding array produc- tions. ...
Splicing Context-Free Matrix Grammars using Parallel Communicating Grammar Systems
2019
VOLUME-8 ISSUE-10, AUGUST 2019, REGULAR ISSUE
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Extensive research on splicing of strings in DNA computing has established important theoretical results in computational theory. Further, splicing on strings has been extended to arrays in[2]. ...
In this context, we propose, a grammar system, using queries to splice context-free matrix grammars and show that the language generated by this grammar system is incomparable to the language given in ...
INTRODUCTION Matrix grammars were introduced by Siromoney et.al [4, 5] to generate two-dimensional picture arrays to be used in image processing. ...
doi:10.35940/ijitee.l3913.1081219
fatcat:3bu4nstb3ndszntnpj55vovaue
Picture Array Generation Based on Membrane Systems and 2D Context-Free Grammars
2017
Journal of Mathematics and Informatics
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In two-dimensional (2D) language theory, extended 2D context free picture grammar (E2DCFPG) constitutes a theoretical model of picture array generation making use of nonterminal symbols and groups of context-free ...
string grammar rules in rewriting a column or row of nonterminal symbols in a picture array with no priority in the rewriting. ...
In the 2D matrix grammar model introduced in [6] , called context-sensitive matrix grammar (CSMG), there are two phases of derivation. ...
doi:10.22457/jmi.v7a5
fatcat:porzxoshrbgpro5vucox45kefq
Page 1548 of Mathematical Reviews Vol. 49, Issue 4
[page]
1975
Mathematical Reviews
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A terminal string generated by G, is a one-dimensional array. ...
If an m-dimensional array of terminals is generated by G,, ---, G_ (1S m<vn) then it is supposed that any cell of this array contains a start symbol of one of the grammars Gy44,1, °°
8437
dimensional array ...
Pure 2D picture grammars and languages
2009
Discrete Applied Mathematics
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A new syntactic model, called pure two-dimensional (2D) context-free grammar (P2DCFG), is introduced based on the notion of pure context-free string grammar. ...
An analogue of this 2D grammar model called pure 2D hexagonal context-free grammar (P2DHCFG) is also considered to generate hexagonal picture arrays on triangular grids. ...
A preliminary version of the paper was presented at the 12th International Workshop on Combinatorial Image Analysis, Buffalo, NY, USA, April 2008 [33] . ...
doi:10.1016/j.dam.2009.02.017
fatcat:7u4y3pn6djebhgf4stbciiweee
Page 1235 of Mathematical Reviews Vol. 50, Issue 4
[page]
1975
Mathematical Reviews
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An n-dimensional array language is the set of all matrices generated by an n-dimensional array grammar. ...
An n-dimensional array grammar is a device that is able to gener- ate n-dimensional matrices of symbols of a finite alphabet by means of rewriting rules; its definition is too complicated to be reproduced ...
Multiset random context grammars, checkers, and transducers
2007
Theoretical Computer Science
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We introduce a general model of random context multiset grammars as well as the concept of multiset random context checkers and transducers. ...
Array grammars We now introduce the basic notions for n-dimensional arrays and array grammar schemes and array grammars (e.g., see [7, 20, 24] ). Let d ∈ N. ...
A d-dimensional array grammar then is a pair (G A , {(v 0 , S)}) where {(v 0 , S)} is the start array (axiom) with S ∈ N and v 0 ∈ Z d . ...
doi:10.1016/j.tcs.2006.11.022
fatcat:sghcvgzywfcetamziuwxlsrhyq
Picture languages with array rewriting rules
1973
Information and Control
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The grammars describe a wide variety of pictures and are more powerful than the matrix grammars for digital pictures introduced in our earlier paper. ...
Each letter of the alphabet of different sizes can be generated by a context-free array grammar. SIROMONEY, SIROMONEY, AND KRITHIVASAN ...
In this paper we have generalized the notion of rewriting rules in string grammars to array rewriting rules for matrix grammars. ...
doi:10.1016/s0019-9958(73)90573-1
fatcat:plb64ecibnggdgbx7adymgq2le
Generative Aspects of Oxide Pictures by Oxide Tile Rewriting Grammar
2019
International journal of recent technology and engineering
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In a two dimensional plane a ring of tetrahedrons that are shared by Oxygen nodes forms a silicate sheet.In this paper, Oxide Tile Rewriting Grammar (OXTRG) is proposed for generating Oxide pictures. ...
Several studies have been done for generating and/or recognizing higher dimensional objects using formal models. ...
INTRODUCTION In formal languages images can be generated using two dimensional grammars. Two dimensional grammars can be classified as array grammars and matrix grammars respectively. ...
doi:10.35940/ijrte.c4259.098319
fatcat:cckbmotoufbmpkmgryrf2qsps4
Page 433 of Mathematical Reviews Vol. , Issue 87a
[page]
1987
Mathematical Reviews
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(F-CNRS); Siromoney, Rani (6-MDRCC); Siromoney, Gift (6-MDRCC)
A note on an extension of matrix grammars generating two-dimensional languages. Inform. Sci. 35 (1985), no. 3, 223-233. ...
Author summary: “We propose an extended version of the paral- lel/sequential table matrix models, called extended table matrix grammars (Ex-TMG), generating arrays of symbols. ...
A CKY parser for picture grammars
2008
Information Processing Letters
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We study the complexity of the membership or parsing problem for pictures generated by a family of picture grammars: Siromoney's Context-Free Kolam Array grammars (coincident with Matz's context-free picture ...
grammars). ...
A picture on a finite alphabet Σ is a two-dimensional rectangular array of elements in Σ. The size |p| of a picture p is the pair (|p| row , |p| col ) of its number of rows and columns. ...
doi:10.1016/j.ipl.2007.09.002
fatcat:s5nihfpyivgt5mmony4o32vd2e
Einstein summation for multidimensional arrays
2002
Computers and Mathematics with Applications
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one of the most common data structures, at least in scientific computing, is the multidimensional array. ...
Some numerical algorithms may conveniently be expressed as a generalized matrix multiplication, which computes a multidimensional array from two other multidimensional arrays. ...
Here, A is a matrix, representable as an array with two indices, and the unknown z and the right-hand side b are vectors, which can be represented as one-dimensional arrays. ...
doi:10.1016/s0898-1221(02)00210-9
fatcat:vouqlohrlfb5tkmloocgo5lgem
Two-dimensional jumping finite automata
2017
Mathematics for applications
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In this paper, we extend a newly introduced concept called the jumping finite automata for accepting string languages to two-dimensional jumping finite automata for accepting two-dimensional languages. ...
We discuss some of the basic properties of these automata and compare the family of languages accepted by these automata with the family of Siromoney matrix languages and also recognizable picture languages ...
In [20] , Wang presents a new system for generating two-dimensional patterns using matrix grammars and array grammars. This model corresponds to a sequential/parallel system. ...
doi:10.13164/ma.2016.08
fatcat:xxp5wbk7xjb43chk5cvmjqyijy
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