V. Rajkumar Dare

Circular DNA and Splicing Systems

Circular strings representing DNA molecules and certain recombinant behaviour are formalized. Various actions of splicing schemes on linear and circular DNA molecules are examined. It is shown that there is a difference in the regularity result of Culik and Harju [1] between the linear and circular strings. A consequence of this result is that a conjecture of Head [4] that the circular string language of a splicing system under an action on circular strings is regular, when the set of initial circular strings is regular, is disproved.

INFINITE ARRAYS AND INFINITE COMPUTATIONS

Abstract A complete metric topology is introduced on the set of all finite and infinite arrays and the topological properties of the space are studied. In this complete metric topology, infinite arrays are the limits of increasing sequences of finite arrays. The notion of successful infinite derivations in Generalized Context-free Kolam Array Grammars, yielding infinite arrays, is a subclass of Generalized context-free kolam array grammars. For this class, the finite array language generated by a reduced grammar in Greibach normal form and the set of infinite arrays generated by it are related through the notion of adherence.

On infinite words obtained by selective substitution grammars

Abstract We present a method of generating infinite words from selective substitution grammars introduced by Rozenberg (1977). Comparison is made with some of the well-known limiting processes and limit language families and certain closure properties are examined. A technique is given for obtaining infinite non-repetitive words. Several decidability results are established.

Infinite arrays and controlled deterministic table 0L array systems

Abstract Deterministic table 0L array systems with control are considered for the generation of infinite arrays. Rewriting of a rectangular array is done in parallel by a table of rules, the rightmost edge horizontally or the lowermost edge vertically downwards. The application of the tables is controlled by a control set. Cube-free and square-free infinite arrays are obtained as an application of this model. The adherence of the array language of a controlled deterministic table 0L array system is related to the adherence of its control set. The limit language equivalence problem and the adherence equivalence problem are shown to be undecidable for this system.

Learning of recognizable picture languages

Learning of certain classes of two-dimensional picture languages is considered. Linear time algorithms that learn in the limit, from positive data the classes of local picture languages and locally testable picture languages are presented. A crucial step for obtaining the learning algorithm for local picture languages is an explicit construction of a two-dimensional on-line tessellation acceptor for a given local picture language. An efficient algorithm that learns the class of recognizable picture languages from positve data and restricted subset queries, is presented in contrast to the fact that this class is not learnable in the limit from positive data alone.

A Study on Diminishing Cells Infinite Array

In this paper we introduce an infinite array with diminishing cells and study some of their combinatorial properties. We call this array as Dr array. A code space can be reorganized in an endless variety of amazing geometrical and topological ways to form sets that look like leaves, ferns, cells, flowers and so on. For this we introduce a complete metric in Dr array. We note that this space is in fact compact. Also certain properties of Dr array are obtained.

A Generalization of the Parikh Vector for Finite and Infinite Words

A metric is defined on the set of all finite and infinite words based on the difference between the occurrences of different letters of the alphabet. This induces a topology which coincides with the metric topology defined by Nivat [5]. Using this metric a vector is defined which gives rise to the position vector p showing the position in the word of each letter of the alphabet. The p-vector can be regarded as a generalization of the Parikh vector [6]. While the Parikh vector of a word enumerates the number of occurrences of each letter of the alphabet, the p-vector introduced in this paper indicates the positions of each letter of the alphabet in the word. Also, the Parikh vector is defined for finite words and the p-vector gives a generalization to infite words. The p-vector has nice mathematical properties. Characterizations of regular sets, context-free languages and a few families from Lindenmayer systems are given.

Bordered Infinite Words

In this paper, we define θ—bordered infinite word and unbordered words and study their properties. We give a characterization of \( \theta \)—bordered infinite words for an antimorphic involution θ. We show that the limit language of the set of all θ—bordered words is a ω—regular language for an antimorphic involution θ.

Bordered Factors of a Finite Word

In this paper, we define

Thue Systems and DNA - A Learning Algorithm for a Subclass

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