Kamala Krithivasan

Abstract families of matrices and picture languages

A linguistic model to generate matrices (arrays of terminals) is presented. The sixclosure axioms which define abstract families of languages (AFL) are extended to matrices to obtain abstract families of matrices (AFM). Corresponding automata to recognize matrices are defined and equivalence established. Immediate application is shown in picture processing by generating a wide class of interesting pictures. Illustrations include generation of kolam patterns, wall paper designs and geometric patterns replicated several times. Simple transformations of a picture such as reflection, translation, halftum, and turning upside down are very naturally obtained.

Picture languages with array rewriting rules

Generative models of picture languages with array rewriting rules are presented. The rewriting rules are regular, context-free or context-sensitive with arrays of terminals in the place of strings of terminals. Derivations are restricted by the condition for row and column catenation. The grammars describe a wide variety of pictures and are more powerful than the matrix grammars for digital pictures introduced in our earlier paper. A distinct hierarchy is shown to exist between the different classes introduced. The models are closed under reflection (about base and rightmost vertical), halfturn, quarter-turn, transpose, and conjugation. Further closure properties such as union, product, star and homomorphism are examined. The models can be applied to generate several interesting patterns of kolam and to describe the repetitive patterns of two-dimensional crystallography. Each letter of the alphabet of different sizes can be generated by a context-free array grammar.

Array Grammars and Kolam

Kolam designs of South Indian folk art are treated as examples of two-dimensional picture languages, Many of the complicated kolain patterns are seen to be generable by context-free array grammars. Two methods of kolam generation are discussed. One method is to generate the kolam patterns by array grammars with a finite number of primitives as terminals. The other is to generate labeled dots by array grammars and then to give a finite number of simple instructions to draw the kolam pattern on the framework of labeled dots.

Parallel context-free languages

Parallel context-free languages are generated by context-free grammars in which every occurrence of a nonterminal in a line of derivation is rewritten simultaneously by the same rule. It is shown that the intersection of parallel context-free languages and context-free languages is the class of derivationbounded languages. Also, the parallel context-free languages form a proper subclass of the context-sensitive languages and are closed under union, product, Kleene closure, and homomorphism. An intercalation theorem is proved for parallel context-free languages.

P Systems with Membrane Creation: Universality and Efficiency

P systems, introduced by Gh. Paun form a new class of distributed computing model. Several variants of P systems were already shown to be computationally universal. In this paper, we propose a new variant of P systems, P systems with membrane creation, in which some objects are productive and create membranes. This new variant of P systems is capable of solving the Hamiltonian Path Problem in linear time. We show that P systems with membrane creation are computationally complete.

Array automata and operations on array languages

Array automata acting on scenes (two dimensional tapes) are defined. The set of scenes accepted by array automata are proved to be equivalent to the set of arrays generated by array grammars. Certain operators like substitution, homomorphic replication and insertion are extended to sets of arrays. These operators yield interesting classes of pictures.

ON STRING LANGUAGES GENERATED BY SPIKING NEURAL P SYSTEMS WITH ANTI-SPIKES

An Spiking Neural P system with anti-spikes uses two types of objects called spikes and anti-spikes which can encode binary digits in a natural way. The step when system emits a spike or an anti-spike is associated with symbol 1 and 0, respectively. Here we consider these computing devices as language generators. They allow non-determinism between the rules ac → a and ac → ā, c ϵ ℕ, thus help to generate languages which cannot be generated using simple SN P systems.

LOCAL AND RECOGNIZABLE HEXAGONAL PICTURE LANGUAGES

In this paper we consider hexagonal arrays on triangular grids and introduce hexagonal local picture languages and hexagonal tiling systems defining hexagonal recognizable picture languages, motivated by an analogous study of rectangular arrays by Giammarresi and Restivo. We also introduce hexagonal Wang tiles to define hexagonal Wang systems (HWS) as a formalism to describe hexagonal picture languages. It is noticed that the family of hexagonal picture languages defined by hexagonal Wang systems and the family recognized by hexagonal tiling systems coincide. Analogous to hv-domino systems describing rectangular arrays, we define xyz-domino systems and prove that recognizable hexagonal picture languages are characterized as projections of xyz-local picture languages.

Contextual array P systems

We define external and internal array contextual P systems, which generate rectangular arrays. We also introduce external array contextual P systems with erased contexts. Some properties of these systems are discussed. We obtain the relation between external array contextual P systems and external array contextual grammars with regular control.

Returning and non-returning parallel communicating finite automata are equivalent

A parallel communicating automata system consists of several automata working independently in parallel and communicating with each other by request with the aim of recognizing a word. Rather surprisingly, returning parallel communicating finite automata systems are equivalent to the non-returning variants. We show this result by proving the equivalence of both with multihead finite automata. Some open problems are finally formulated.