Abstract A new model of computation called Watson–Crick jumping finite automata was introduced by Mahalingam et al., and the authors study the computing power and closure properties of the variants of the model. There are four variants of the model: no state, 1-limited, all-final and simple Watson–Crick jumping finite automata. In this paper, we introduce a restricted version that is a combination of variants of the existing model. It becomes essential to explore the computing power and closure properties of these combinations. The combination variants are extensively compared with Chomsky hierarchy, general jumping finite automata family and among themselves. We also explore the closure properties of such restricted automata.

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.

In this paper, a novel image encryption scheme is proposed based on permutation-diffusion architecture using cellular automata. In the permutation phase, Wolfram class III radius 2 cellular automata rules are utilized for shuffling the pixels of the plain image and in the diffusion phase; the rules based on unity attractors of elementary cellular automata are employed to encrypt the pixels of the shuffled plain image. Addition to the encryption scheme, a new non-parametric statistical method for measuring the pixel randomness in the shuffled and encrypted images is also proposed in this paper. The strength of the proposed image encryption scheme is first assessed by standard methods for security analysis, and the pixel randomness is then determined by the newly proposed non-parametric method. The results of the assessment exhibit the high security of the diffusion process and its computational efficiency. Copyright © 2016 John Wiley & Sons, Ltd.

Here we continue the study of bio-Turing machines introduced in [2] and further investigated in [17]. We introduce a restricted model of bio-Turing machine and we investigate its computational power, a hierarchy of languages accepted, and deterministic and nondeterministic variants. A comprehensive example illustrating the modelling power of the introduced machine ends the paper.

Self-assembly is a process in which simple objects autonomously combine themselves into larger objects. It is considered as a promising technique in nano-technology. In this paper, we propose a graph-based self-assembly model. Two simple graphsG1andG2with a vertex of common degree overlap and a new self-assembled graph is formed. Besides studying the properties of these self assembled graphs, we answer the question: can a given set of graphs be generated through the process of self-assembly? If so, how to find the generator that could generate the given set of graphs by the process of self-assembly. The question of the existence of the minimal generator is also discussed. The necessary and sufficient condition for a graphHto be obtained by the iterated self-assembly of the graphGis also answered. We also conclude that the problem of finding the generator is decidable.

Array contextual grammars are new array models obtained by inserting arrays columnwise. Even though the growth is restricted to one direction, this array model is capable of generating pictures. Some interesting properties were given using column boundedness and bounded column length increase. An array model of cooperative type called column contextual array hybrid grammar is introduced; closure properties of these two models are investigated.

Terminal weights are attached to L-systems by replacing each terminal generated by an OL-system by fa(i) in the ith step of a derivation. The family of terminal weighted OL languages will be equal to the recursively enumerable set. Terminal weights are attached to EOL-regular matrix languages and also to OL array languages. Parquet deformations are generated by TWEOL-RMS.