Showing papers by "Kalpana Mahalingam published in 2018"

Properties of Parikh Matrices of Binary Words Obtained by an Extension of a Restricted Shuffle Operator

Abstract: We introduce an extension of the restricted shuffle operator on binary words considered by Atanasiu and Teh (2016). We then derive properties on Parikh matrix equivalence of words over a binary alp...

On Derivation Languages of a Class of Splicing Systems

Abstract: Derivation languages are language theoretical tools that describe halting derivation processes of a generating device. We consider two types of derivation languages, namely Szilard and control languages for splicing systems where iterated splicing is done in non-uniform way defined by Mitrana, Petre and Rogojin in 2010. The families of Szilard (rules and labels are mapped in a one to one manner) and control (more than one rule can share the same label) languages generated by splicing systems of this type are then compared with the family of languages in the Chomsky hierarchy. We show that context-free languages can be generated as Szilard and control languages and any non-empty context-free language is a morphic image of the Szilard language of this type of system with finite set of rules and axioms. Moreover, we show that these systems with finite set of axioms and regular set of rules are capable of generating any recursively enumerable language as a control language.

Two-dimensional picture arrays and Parikh q-matrices

Abstract: Based on the idea of “q−count” of certain subwords of a word and generalizing the notion of Parikh matrix of a word, the notion of Parikh q−matrix of a word over an ordered alphabet was introduced. On the other hand, with a two-dimensional picture array of symbols arranged in rows and columns, two kinds of upper triangular matrices, known as row and column Parikh matrices have also been introduced and investigated. Here combining these two kinds of matrices of a picture array, we introduce row/column Parikh q−matrix of an array, leading to the concept of q−ambiguity of a picture array. Results relating to q−ambiguity of picture arrays are derived in the context of these Parikh q−matrices of arrays.

Labelled graph rules in P systems

Abstract: P systems with graph productions were introduced by Freund in 2004. It was shown that such a variant of P system can generate any recursively enumerable language of weakly connected graphs. In this paper, we consider such P systems where the input is any connected graph and each graph production is labelled over an alphabet. We name the system as Process Guided P System where the computation is guided by a string over the set of labels. The set of all strings over the label alphabet which results in the halting computation of the system forms a guiding language of the system. We compare such guiding languages with Chomsky hierarchy. Two direct applications of this variant are also given.

Relative Watson-Crick Primitivity of Words.

Abstract: We introduce the concept of relative Watson-Crick primitivity of words and its generalization, the relative θ-primitivity of words, where θ is a morphic or an antimorphic involution. Similar to relatively prime integers which do not share any common factors, we call two words u and v relatively θ-primitive if they do not share a common θ-primitive root. We study some combinatorial properties of relatively θ-primitive words, as well as establish relations between each of the two words u and v and the result of some binary word operation between u and v, from this perspective.