Raghavan Rama

Tissue P Systems with Contextual and Rewriting Rules

The study of tissue P systems was initiated in [6], inspired from the way neurons cooperate, processing impulses in the complex net established by synapses. These systems use multisets of objects for processing, and it was shown that computational completeness can be achieved using a small number of cells and states. In this paper, we use string objects as the underlying data structure. The control structure used is a restricted form of contextual rules and rewriting rules. We obtain two characterizations of recursively enumerable languages using these systems: tP systems having 2 states and 2 cells as well as tP systems having 4 states and a single cell generate all recursively enumerable languages. We also discuss the relationships with ETOL and EOL languages.

APPROXIMATE BLOCK SORTING

We consider the problem BLOCK-SORTING: Given a permutation, sort it by using a minimum number of block moves, where a block is a maximal substring of the permutation which is also a substring of th...

Breaking DES using P systems

Membrane systems, also called P systems, were introduced by Gh. P?un, as a new class of biologically inspired distributed computing models. Several variants of P systems were already shown to be computationally universal. One of these variants, introduced in Gh. P?un (J. Automata Languages Combin. 6 (1) (2001) 75), is able to solve SAT in linear time. In this paper, we show how this class of P systems (with membrane division) can theoretically break the most widely used cryptosystem, DES. We prove that given an arbitrary (plain-text, cipher-text) pair, one can recover the DES key in linear time with respect to the length of the key.

Array Splicing Systems

In this paper the concept of splicing is extended to arrays and array or 2D splicing systems are defined. Various subclasses of 2D splicing systems are defined and a restricted class viz. finite simple splicing systems is studied. The hierarchy among the various subclasses of finite simple splicing systems and their relationship to the strictly locally testable languages are established.

Merging and Sorting By Strip Moves

We consider two problems related to the well-studied sorting by transpositions problem: (1) Given a permutation, sort it by moving a minimum number of strips, where a strip is a maximal substring of the permutation which is also a substring of the identity permutation, and (2) Given a set of increasing sequences of distinct elements, merge them into one increasing sequence with a minimum number of strip moves. We show that the merging by strip moves problem has a polynomial time algorithm. Using this, we give a 2-approximation algorithm for the sorting by strip moves problem. We also observe that the sorting by strip moves problem, as well as the sorting by transpositions problem, are fixed-parameter-tractable.

Insertion-Deletion P Systems

New computability models, called P systems, based on the evolution of objects in a membrane structure were recently introduced. This paper presents a new variant of P systems with string objects having insertion-deletion rules as the control structure. The use of this control structure is motivated from the DNA Computing area where insertions and deletions of small strands of DNA happen frequently in all types of cells and constitute also one of the methods used by some viri to infect a host. We investigate here the power of this type of systems with less than four membranes, in comparison with the families of CF, MAT and RE.

Towards constructing optimal Strip Move Sequences

The Sorting by Strip Moves problem, SBSM, was introduced in [6] as a variant of the well-known Sorting by Transpositions problem. A restriction called Block Sorting was shown in [2] to be NP-hard. In this article, we improve upon the ideas used in [6] to obtain a combinatorial characterization of the optimal solutions of SBSM. Using this, we show that a strip move which results in a permutation of two or three fewer strips or which exchanges a pair of adjacent strips to merge them into a single strip necessarily reduces the strip move distance. We also establish that the strip move diameter for permutations of size n is n–1. Further, we exhibit an optimum-preserving equivalence between SBSM and the Common Substring Removals problem (CSR) – a natural combinatorial puzzle. As a consequence, we show that sorting a permutation via strip moves is as hard (or as easy) as sorting its inverse.

On generating trees by P systems with active membranes

In this paper, we consider P systems with membrane creation working with symbol objects. As a result of a halting computation we do not take the set of numbers generated in a designated output membrane, instead we take the resulting tree representing the membrane structure of the final configuration. We prove that each recursively enumerable tree language can be obtained by this system.

Chomsky Hierarchy Control on Isotonic Array P Systems

In this paper, we propose a new regulated evolution in P systems with isotonic arrays and isotonic array rules. The regulated language will be a language of Chomsky hierarchy. This model generates interesting pictures for a given regulated language. The generative capacity is explored.

Contextual array splicing systems

The concept of splicing is extended to arrays. A new method of splicing called Contextual Array Splicing is introduced which produces imperfect molecules throughout the structure. This model is capable of generating interesting patterns. We prove that if an array language is p-column strictly locally testable, then all arrays of column size p are constants. The concept of Mixed Splicing is also introduced and an important relation between uniform and equal splicing systems has been proved. We also present some interesting properties of contextual array splicing systems.