Author

# K. Lakshmanan

Bio: K. Lakshmanan is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topic(s): Context-sensitive grammar & Tree-adjoining grammar. The author has an hindex of 2, co-authored 2 publication(s) receiving 15 citation(s).

Topics: Context-sensitive grammar, Tree-adjoining grammar, String (computer science), Recursively enumerable language, Embedded pushdown automaton

##### Papers

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TL;DR: P Systems with string objects which evolve by means of one-sided contextual rules and erasing contextual rules are considered, and it is shown that systems with three membranes characterize the family of recursively enumerable languages.

Abstract: We consider P Systems with string objects which evolve by means of one-sided contextual rules and erasing contextual rules. The generative power of these systems with three or less than three membranes is investigated. We show that systems with three membranes characterize the family of recursively enumerable languages. When the string replication is used in one-sided contextual rules, these systems are able of solving NP-complete problems in linear time: this is exemplified with SAT and HPP.

8 citations

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TL;DR: A restricted version of depth-first contextual grammars, which depends on length of the inserting contexts, is considered, which gives a solution to the open problem P14 listed in [8].

Abstract: In this paper, we introduce some new variants of contextual grammars and investigate their generative power. We'consider a restricted version of depth-first contextual grammars, which depends on length of the inserting contexts. Using this variant, we give a solution to the open problem P14 listed in [8]. We also introduce random context contextual grammars and compare its generative power with the families IC , ICC , EC , ECC , TC . Time-varying contextual grammars are introduced which resemble time-varying grammars. We compare the generative power of this variant with the families of internal, external, total, matrix, and programmed contextual grammars.

7 citations

##### Cited by

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TL;DR: This work investigates a variant of purely communicating P systems, where multisets of activators can open channels for certain objects to pass through membranes in one direction, and shows that for such systems with only one membrane and using only singleton activator and prohibitor sets, universal computational power is obtained.

Abstract: We investigate a variant of purely communicating P systems, where multisets of activators can open channels for certain objects to pass through membranes in one direction; however, the permeability of a channel can be controlled by multisets of prohibitors, too.We will show that for such systems with only one membrane and using only singleton activator and prohibitor sets, we already obtain universal computational power. When using systems with activating multisets for membrane channels only, we obtain a similar result. By showing a close correspondence to P systems with symport/antiport as introduced in [13] we can optimize some results given there.

47 citations

01 Jan 2007

TL;DR: The present notes intend to survey the research related to some of the problems of membrane computing, mentioning both progresses made in solving them and questions which still wait for research efiorts.

Abstract: Membrane computing is a branch of natural computing aiming to abstract computing models from the structure and functioning of the living cell, and from the way cells cooperate in tissues, organs, or other populations of cells. This research area developed very fast, both at the theoretical level and in what concerns the applications. During the almost ten years since membrane computing was initiated, several open problems were circulated, sometimes in comprehensive lists prepared for meetings in this area. The present notes intend to survey the research related to some of these problems, mentioning both progresses made in solving them and questions which still wait for research efiorts.

26 citations

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TL;DR: The hierarchy of language families of contextual languages which is obtained by the use of nilpotent, combinational, definite, regular suffix closed, and regular commutative languages as choice languages is determined.

Abstract: We discuss external contextual grammars with choice where the choice language belongs to a family of subregular languages. We determine the hierarchy of language families of contextual languages which is obtained by the use of nilpotent, combinational, definite, regular suffix closed, and regular commutative languages as choice languages.

9 citations

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TL;DR: This paper improves a universality result avoiding the extended feature and by using rules of small weight in contextual P systems and has two (rather surprising) universality results, both of them using three membranes for non-extended systems with replicated rewriting and with leftmost rewriting.

Abstract: In this paper, we continue the study of contextual and rewriting P systems. In contextual P systems, we improve a universality result avoiding the extended feature and by using rules of small weight. In rewriting P systems, we have two (rather surprising) universality results, both of them using three membranes, for non-extended systems with replicated rewriting and with leftmost rewriting, respectively.

7 citations

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TL;DR: This work considers a P system with only alphabetic flat splicing rules as the evolution rules and strings of symbols as objects in its regions and shows that AFS P systems with two membranes are more powerful in generative power than AFSP systems with a single membrane.

Abstract: An operation on strings, called flat splicing was introduced, inspired by a splicing operation on circular strings considered in the study of modelling of the recombinant behaviour of DNA molecules. A simple kind of flat splicing, called alphabetic flat splicing, allows insertion of a word with a specified start symbol and/or a specified end symbol, between two pre-determined symbols in a given word. In this work, we consider a P system with only alphabetic flat splicing rules as the evolution rules and strings of symbols as objects in its regions. We examine the language generative power of the resulting alphabetic flat splicing P systems (AFS P systems, for short). In particular, we show that AFS P systems with two membranes are more powerful in generative power than AFS P systems with a single membrane. We also construct AFS P systems with at most three membranes to generate languages that do not belong to certain other language classes and show an application to generation of chain code pictures.

6 citations