V. R. Dare

Chennai Mathematical Institute

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N. Jansirani

University of Madras

Rani Siromoney

Chennai Mathematical Institute

D. G. Thomas

Saveetha University

R. Arulprakasam

SRM Institute of Science and Technology

K. G. Subramanian

Liverpool Hope University

T. Kalyani

Kalasalingam Academy of Research and Education

A. Saoudi

Northern Border University

N. Vijayaraghavan

Vellore Institute of Technology University

S. Annadurai

St. Joseph’s College of Engineering

R. Krishna Kumari

SRM Institute of Science and Technology

Cooperative Institutions

University of Madras

SRM Institute of Science and Technology

Karnatak University

Anna University, Chennai

St. Joseph's Institute of Technology

St. Joseph’s College of Engineering

Saint Joseph's College

Vellore Institute of Technology University

Centre National de la Recherche Scientifique

Sri Venkateswara University

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Generalized Parikh matrices of picture array

J. Math. Comput. Sci. (2021)

K. Janaki R. Arulprakasam V. R. Dare

The theory of Parikh matrices and subword occurrences has led to extensive research in combinatorics on words. The extension of Parikh matrix of a word into picture array is an another interesting problem. Since the Parikh matrix does not say about the number of subword occurrences in the array. Therefore, in this paper we introduce the generalized Parikh matrix of a picture array which gives the number of subwords occurrences in the array. We also discuss some properties of generalized Parikh matrices.

Matrix (chemical analysis)

10.28919/10.28919/jmcs/5482

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RIPPLES HAMILTONIAN GRAPH

Advances in Mathematics Scientific Journal (2021)

Rama Raghavan N. Jansirani V. R. Dare

Hamiltonian (control theory)

10.37418/amsj.10.3.44

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Rough Finite State Automata and Rough Languages

Journal of Physics Conference Series (2018)

R. Arulprakasam R. Perumal M. Radhakrishnan V. R. Dare

Sumita Basu [1, 2] recently introduced the concept of a rough finite state (semi)automaton, rough grammar and rough languages. Motivated by the work of [1, 2], in this paper, we investigate some closure properties of rough regular languages and establish the equivalence between the classes of rough languages generated by rough grammar and the classes of rough regular languages accepted by rough finite automaton.

Closure (psychology)

Deterministic finite automaton

Probabilistic automaton

Regular language

10.1088/1742-6596/1000/1/012155

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Special inverses of k− Modulo infinite array

AIP conference proceedings (2022)

N. Jansirani V. Subharani V. R. Dare

In this research article, k — Modulo Infinite Array and Complement of k — Modulo Infinite Array are introduced. The algebraic and Circulant properties for k — Modulo Infinite Array and Complement of k — Modulo Infinite Array are deliberated. The Norm and Spectrum of k — Modulo Infinite Array are derived and generalized for any dimension. The Generalized inverse is existed for k — Modulo Infinite Array and Complement of k — Modulo Infinite Array and also the Special inverses are elaborated. The subarrays of k — Modulo Infinite Array and Complement of k — Modulo Infinite Array have inherited the existence of Special inverses such as Quasi Commuting inverse, Drazin inverse and Group inverse, which are explored with suitable numerical illustrations.

Modulo operation

Complement

Multiplicative inverse

Orthogonal complement

10.1063/5.0103933

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WATSON CRICK FUZZY AUTOMATA WITH OUTPUT

Advances in Mathematics Scientific Journal (2021)

N. Vijayaraghavan N. Jansirani V. R. Dare

Watson

10.37418/amsj.10.3.47

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Language properties and Grammar of Parallel and Series Parallel Languages

arXiv (Cornell University) (2017)

N. Mohana Kalyani Desikan V. R. Dare

In this paper we have defined the language theoretical properties of Parallel languages and series parallel languages. Parallel languages and Series parallel languages play vital roles in parallel processing and many applications in computer programming. We have defined regular expressions and context free grammar for parallel and series parallel languages based on sequential languages [2]. We have also discussed the recognizability of parallel and series parallel languages using regular expression and regular grammar.

Parallel programming model

10.48550/arxiv.1711.01799

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Parikh prime vector in partial word

AIP conference proceedings (2020)

K. Janaki R. Arulprakasam V. R. Dare

If the gcd of the components of n-dimensional vector of natural numbers is one,then it is considered to be prime. A Parikh prime word has a Parikh prime Vector. In this paper the notion of Parikh Prime for Partial words and Generalized Parikh Prime for Partial word is defined along with few properties and the association between them is analysed.

10.1063/5.0025325

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Partial Petri Net Languages and their Properties

International Journal of Information Technology (2024)

A. Mahadeer R. Arulprakasam V. R. Dare

Net (polyhedron)

Stochastic Petri net

Closure (psychology)

10.1007/s41870-024-01903-0

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Two dimensional rough online Tesselation automaton and its properties

J. Math. Comput. Sci. (2021)

N. Vijayaraghavan N. Jansirani V. R. Dare

The concept of rough set theory was introduced in Formal Languages and Automata theory to find Rough Automata, Rough Languages and Rough Grammar. Rough Automata theory can be recognized as an efficient mathematical model in Machine learning and Data mining. In this research article, the rough sets notion is introduced in two dimensional automata theory. Rough set idea is incorporated in Two Dimensional Four Way Finite State Automata and Two Dimensional Online Tesselation Automata to give Two Dimensional Four Way Rough Finite state Automata and Two Dimensional Rough Online Tesselation Automata respectively. The Rough transition map extension of Two Dimensional Rough Online Tesselation Automata is done. The characterizations of Two Dimensional Rough Online Tesselation Automata are studied. Closure properties of Rough Languages recognized by Two Dimensional Rough Online Tesselation Automata under Boolean operations are obtained. Finally the relationship between Two Dimensional Four Way Rough Finite state Automata and Two Dimensional Rough Online Tesselation Automata is established.

10.28919/10.28919/jmcs/5739

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PARALLEL GENERATION OF FINITE IMAGES

International Journal of Pattern Recognition and Artificial Intelligence (1989)

Maurice Nivat A. Saoudi V. R. Dare

We define a syntactic model for generating sets of images, where an image can be viewed as an array over finite alphabet. This model is called image grammar. Image grammar can be considered as a generalization of classical Chomsky grammar. Then we study some combinatorial and language theoretical properties such as reduction, pumping lemmas, complexity measure, we give a strict infinite hierarchy. We also characterize these families in terms of deterministic substitutions and Chomsky languages.

Chomsky hierarchy

10.1142/s0218001489000243

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Citations (15)