T. Kalyani

Local and Recognizable Iso Picture Languages

In the context of a syntactic approach to pattern recognition, there have been several studies in the last few decades on theoretical models for generating or recognizing two-dimensional objects, pictures and picture languages. Motivated by these studies we introduce a new notion of recognizability for a class of picture languages called iso picture languages. We first introduce a notion of local iso picture language and then define a recognizable iso picture language as a projection of a local iso picture language. We prove certain closure properties of this family of languages. We present a learning algorithm LOC for local iso picture languages.

Iso-array acceptors and learning

The notions of iso-arrays, iso-pictures, local iso-picture languages and recognizable iso-picture languages have been introduced and studied in [6]. In [6] we have provided an algorithm to learn local iso-picture languages through identification in the limit using positive data. In this paper, we construct a two-dimensional on-line tessellation automaton to recognize iso-picture languages and present an algorithm to learn recognizable iso-picture languages from positive data and restricted subset queries.

Results on Hexagonal Tile Rewriting Grammars

Tile rewriting grammars are a new model for defining picture languages. In this paper we propose hexagonal tile rewriting grammars (HTRG) for generating hexagonal picture languages. Closure properties of HTRG are proved for some basic operations. We compare HTRG with hexagonal tiling systems.

Partial Commutation on Array Languages

Algebraic characterization of recognizable trace languages were studied and the relation of recognizable trace languages to elementary Petri nets were established by using partial commutation as a tool. Motivated by the above studies in string languages, we have extended the notion of partial commutation to two-dimensional array languages and established that if L is local then φ(L) need not be local, where φ is a partial commutation mapping. We have proved that L(φ(θ)) and φ(L(θ)) are not disjoint, where θ is a finite set of 2 ×2 tiles over the alphabet Γ ∪ {#}. We have also considered partial commutation mapping on Siromoney matrix languages and proved some interesting results.

Rewriting P systems generating iso-picture languages

Membrane Computing is a branch of natural computing aiming to abstract computing ideas for the structure and the functioning of living cells as well as from the way the cells are organized in tissues or higher order structures. We consider iso-picture languages introduced in [2,3] and the possibility to handle them with P systems. In this paper we introduce regular iso-array rewriting P system, context-free iso-array rewriting P system and Basic puzzle iso- array rewriting P system and they are compared for generative power.

Collage of Hexagonal Arrays

A new operation called collage on one-dimensional (respectively two-dimensional) word languages was introduced in [2]. It is obtained by piling up, one on top of the other, words of a given recognizable language on a previously empty one-dimensional (respectively two-dimensional) array. In this paper we extend this operation to hexagonal picture languages, and show that if P is a hexagonal picture language over one letter alphabet then Collage (P ) is recognizable.

Shuffle on trajectories over finite array languages

Parallel composition of words and languages of words appear as a fundamental operation in parallel computation and in the theory of concurrency. Shuffle on trajectories provides a method to handle the operation of parallel composition. In this paper we study the impact of shuffle on trajectories on various finite arrays. We obtain interesting results yielding new pictures and patterns. We compare this model with the other existing models.

Online tessellation automaton recognizing various classes of convex polyominoes

A polyomino is a finite connected union of cells having no cut points. Tiling and Wang recognizability of convex polyominoes have been studied in detail by De Carli et al. In this paper we define 2D polyomino online tessellation automaton to recognize a class of polyominoes and prove that the family of various classes of polyominoes recognized by tiling systems and 2D-polyomino online tessellation automata coincide. We also study the recognizability of convex polyominoes by domino systems.

Collage of iso-picture languages and P -systems

A new operation called collage on one-dimensional (respectively two-dimensional) word languages, obtained by piling up, one on top of the other, words of a given recognizable language on a previously empty one-dimensional (respectively two-dimensional) array, was introduced (2005). In this paper we extend the operation to iso-picture languages. We show that if L is an iso-picture language over a two letter alphabet then collage of L is recognizable. We introduce a new P system which consists of membrane structure in which the object in each membrane is a collection of iso-picture languages and the evolutionary rules are given in terms of collage operations. We obtain some properties of this P system using recognizability of collage of L.

t-communicating iso-array P system

Membrane computing (P systems), is an interesting area of research in the study of formal string language theory in recent years. Many deep results have been obtained in this study. Recently iso-array rewriting P systems have been developed in the context of two-dimensional picture description. In this paper, we introduce iso-array rewriting P system with t-communication and analyze the power of this system and compare it with the other systems developed earlier by the authors.