Ajeesh Ramanujan

Bio: Ajeesh Ramanujan is an academic researcher from APJ Abdul Kalam Technological University. The author has contributed to research in topics: Recursively enumerable language & String (computer science). The author has an hindex of 4, co-authored 9 publications receiving 54 citations. Previous affiliations of Ajeesh Ramanujan include Indian Institute of Technology Madras.

On Controlled P Systems

Abstract: We introduce and briefly investigate P systems with controlled computations. First, P systems with label restricted transitions are considered in each step, all rules used have either the same label, or, possibly, the empty label, λ, then P systems with the computations controlled by languages as in context-free controlled grammars. The relationships between the families of sets of numbers computed by the various classes of controlled P systems are investigated, also comparing them with length sets of languages in Chomsky and Lindenmayer hierarchies characterizations of the length sets of ET0L and of recursively enumerable languages are obtained in this framework. A series of open problems and research topics are formulated.

On Controlled P Systems

Abstract: We introduce and briefly investigate P systems with controlled computations. First, P systems with label restricted transitions are considered in each step, all rules used have either the same label, or, possibly, the empty label, λ, then P systems with the computations controlled by languages as in context-free controlled grammars. The relationships between the families of sets of numbers computed by the various classes of controlled P systems are investigated, also comparing them with length sets of languages in Chomsky and Lindenmayer hierarchies characterizations of the length sets of ET0L and of recursively enumerable languages are obtained in this framework. A series of open problems and research topics are formulated.

Control Words of Transition P Systems

Abstract: A new way of associating a language with the computation of a P system is considered. A label is assigned to every rule in a P system, where the labels are chosen from a finite alphabet or \(\lambda .\) We associate a string, called control word, that is obtained by concatenating the labels of the rules in the transition sequence corresponding to a computation. We study the generative capacity of such control languages comparing them with family of languages such as regular, context-free, context-sensitive and recursively enumerable languages of Chomskian hierarchy.

Control Languages Associated with Tissue P Systems

Abstract: We consider a way to associate a language with the computations of a tissue P system. We assign a label to every rule, where the labels are chosen from an alphabet or the label can be λ. The rules used in a transition should have either the empty label or the same label from the chosen alphabet. In this way, a string is associated with each halting computation, called the control word of the computation. The set of all control words associated with computations in a tP system form the control language of the system. We study the family of control languages of tP systems in comparison with the families of finite, regular, context-free, context-sensitive, and recursively enumerable languages.

Ramanujan sums based image kernels for computer vision

Abstract: In the recent history, kernel methods had established themselves as powerful tools for computer vision. In this paper we introduce an integer image kernel function based on Ramanujan Sums which finds its place in image vision. The paper proves the validity of kernel function theoretically and also shows the application of the kernel in image vision. Ramanujan Sums are based on number theory and hence the new kernel matrix will contain only the integer values. Since the image processing involves complex matrix manipulations, the processing based on the new kernel will be computationally effective. The paper shows the applicability of the kernel in various context of image processing. By applying the theory of Ramanujan Sums for image kernel, we will show the intervention of numerical mathematics in machine learning which gives new directions for future research.

Computational power of tissue P systems for generating control languages

Abstract: Tissue P systems are a class of distributed and parallel models of computation inspired by the way of communication among living cells or between cells and their environment. In this work, we investigate the computational power of tissue P systems, where each rule is assigned either with a label chosen from an alphabet or with the empty label λ . The sequence of labels of rules applied during a halting computation is defined as the result of the computation, and the set of all results computed by a given tissue P system is called a control language. We prove that tissue P systems with antiport rules of weight one and without symport rules characterize regular languages; tissue P systems with antiport rules of weight at most two (resp., symport rules of weight at most two) without symport rules (resp., antiport rules) are universal. Tissue P systems with antiport rules of weight one and symport rules of weight one are also proved to be universal. These results show that the rule complexity is crucial for tissue P systems to achieve a desired computational power.

Spiking neural P systems with homogeneous neurons and synapses

Abstract: Spiking neural P systems (SN P systems, for short) are a class of distributed parallel computing devices inspired from the way neurons process information and communicate by means of spikes, where neurons are different in the sense that they can have different sets of spiking rules. In this work, we consider a variant of SN P systems with two restrictions: (1) all neurons contain only spikes (neurons are homogeneous in this case, since they can be considered as containers of spikes), while the spiking rules are moved on the synapses; (2) all synapses are homogeneous in the sense that each synapse has the same set of rules. These restrictions correspond to the fact that the SN P system consists of only one kind of neurons and one kind of synapses. The computational power of SN P systems with homogeneous neurons and synapses is investigated. Specifically, it is proved that such systems are Turing universal as both number generating and number accepting devices.

How to Obtain Computational Completeness in P Systems with One Catalyst

Abstract: Whether P systems with only one catalyst can already be computationally complete, is still an open problem. Here we establish computational completeness by using specific variants of additional control mechanisms. At each step using only multiset rewriting rules from one set of a finite number of sets of multiset rewriting rules allows for obtaining computational completeness with one catalyst and only one membrane. If the targets are used for choosing the multiset of rules to be applied, for getting computational completeness with only one catalyst more than one membrane is needed. If the available sets of rules change periodically with time, computational completeness can be obtained with one catalyst in one membrane. Moreover, we also improve existing computational completeness results for P systems with mobile catalysts and for P systems with membrane creation.

P Systems Working in Maximal Variants of the Set Derivation Mode

Abstract: In P systems working in the set derivation mode, even in the maximally parallel derivation mode, rules are only applied in at most one copy in each derivation step. We also consider the set mode in the cases of taking those sets of rules with the maximal number of applicable rules or with affecting the maximal number of objects. For many variants of P systems, the computational completeness proofs even literally still hold true for these new set derivation modes. On the other hand, we obtain new results for P systems using target selection for the rules to be chosen together with these set derivation modes.

On Controlled P Systems

Abstract: We introduce and briefly investigate P systems with controlled computations. First, P systems with label restricted transitions are considered in each step, all rules used have either the same label, or, possibly, the empty label, λ, then P systems with the computations controlled by languages as in context-free controlled grammars. The relationships between the families of sets of numbers computed by the various classes of controlled P systems are investigated, also comparing them with length sets of languages in Chomsky and Lindenmayer hierarchies characterizations of the length sets of ET0L and of recursively enumerable languages are obtained in this framework. A series of open problems and research topics are formulated.