Some properties of probabilistic semi-simple splicing systems

The concept of splicing system was first introduced by Head in 1987. This model has been introduced to investigate the recombinant behavior of DNA molecules. Over the years, various types of splicing languages have been defined and studied by different mathematicians. Splicing systems with finite sets of axioms only generate regular languages. Therefore, different restrictions have been considered to increase the computational power up to the recursively enumerable languages. In this research, a variant of splicing systems called probabilistic splicing systems has been used to define different types of splicing systems such as probabilistic simple splicing systems, probabilistic semi-simple splicing systems and probabilistic one-sided splicing systems. In probabilistic splicing systems, probabilities (real numbers in the range of 0 and 1) are associated with the axioms, and the probability p(z)of the string z generated from two strings x and y is calculated from the probability p(x)and p(y) according to the operation *(multiplication) defined on the probabilities, i.e., p(z) = p(x) * p(y)

Weighted simple and semi-simple splicing systems

The modelling of splicing system has been introduced theoretically by Head in 1987. As time goes on, various splicing systems have been developed, such as one-sided, simple and semi-simple splicing systems. However, in the investigation on the generative power of splicing system, there are limitations on the generative power of splicing system with finite components. In order to overcome the limitation of the usual splicing system, one variant of splicing system has been introduced recently, called the weighted splicing system. In this paper, we associate weights from selected weighting spaces to the axioms of simple and semi-simple splicing systems, thus introducing weighted simple splicing system and weighted semi-simple splicing system. Some examples are presented for weighted simple and semi-simple splicing systems to illustrate their generative power. Lastly, relation of the languages generated by weighted simple and semi-simple splicing systems in the Chomsky hierarchy are also investigated

Splicing Systems from Past to Future: Old and New Challenges

A splicing system is a formal model of a recombinant behaviour of sets of double stranded DNA molecules when acted on by restriction enzymes and ligase. In this survey we will concentrate on a specific behaviour of a type of splicing systems, introduced by P\u{a}un and subsequently developed by many researchers in both linear and circular case of splicing definition. In particular, we will present recent results on this topic and how they stimulate new challenging investigations.Comment: Appeared in: Discrete Mathematics and Computer Science. Papers in Memoriam Alexandru Mateescu (1952-2005). The Publishing House of the Romanian Academy, 2014. arXiv admin note: text overlap with arXiv:1112.4897 by other author

Circular Languages Generated by Complete Splicing Systems and Pure Unitary Languages

Circular splicing systems are a formal model of a generative mechanism of circular words, inspired by a recombinant behaviour of circular DNA. Some unanswered questions are related to the computational power of such systems, and finding a characterization of the class of circular languages generated by circular splicing systems is still an open problem. In this paper we solve this problem for complete systems, which are special finite circular splicing systems. We show that a circular language L is generated by a complete system if and only if the set Lin(L) of all words corresponding to L is a pure unitary language generated by a set closed under the conjugacy relation. The class of pure unitary languages was introduced by A. Ehrenfeucht, D. Haussler, G. Rozenberg in 1983, as a subclass of the class of context-free languages, together with a characterization of regular pure unitary languages by means of a decidable property. As a direct consequence, we characterize (regular) circular languages generated by complete systems. We can also decide whether the language generated by a complete system is regular. Finally, we point out that complete systems have the same computational power as finite simple systems, an easy type of circular splicing system defined in the literature from the very beginning, when only one rule is allowed. From our results on complete systems, it follows that finite simple systems generate a class of context-free languages containing non-regular languages, showing the incorrectness of a longstanding result on simple systems

Splicing systems and the Chomsky hierarchy

In this paper, we prove decidability properties and new results on the position of the family of languages generated by (circular) splicing systems within the Chomsky hierarchy. The two main results of the paper are the following. First, we show that it is decidable, given a circular splicing language and a regular language, whether they are equal. Second, we prove the language generated by an alphabetic splicing system is context-free. Alphabetic splicing systems are a generalization of simple and semi-simple splicin systems already considered in the literature

On the new relation of second order limit language and other different types of splicing system

Mathematical modelling of splicing system has been introduced to initiate a linkage between the study of informational macromolecules that includes DNA and formal language theory. The ability to present the nitrogenous base which is a component in a nucleotide of DNA, as a series of alphabet, ignites this interdisciplinary study. Over the years, researchers have developed models to match their need. In addition, product of splicing system is called splicing language. Through some development, second order limit language is derived from other type of languages known as limit language. Its existence and characteristics have been vastly discussed. Beside, some types of splicing system can produce second order limit language. In this research, the characteristics of varieties of splicing system are studied and their relations with second order limit language are established

n-cutting site of DNA splicing language for single string and palindromic rule

A new symbolization of Yusof-Goode (Y-G) splicing system was introduced by Yusof in 2012, is inspired by the framework of Formal Language Theory introduced by Head in 1987. Y-G splicing system is intended to present the biological process of DNA splicing in a translucent way. In this paper, starting with some relevant preliminaries, one theorem is proposed via Y-G approach using one initial string and one rule with different characteristics of the restriction enzyme. Additionally, the theorem showed the behavior of the splicing languages generated at single stage splicing. Two cases are considered in the theorem by conducting splicing using palindromic rule and palindromic recognition site with same left and right context for Case I and different left and right context for Case II. Furthermore, two molecular examples are discussed to validate two cases proposed in the theorem, which shows the real meaning of the theorem in biological aspect. From the proposed theorem, based on the splicing language generated, the type of splicing language can be determined. It is discovered that, the generated languages are in the form of limit and transient

GRAPHICAL USER INTERFACE FOR BOUNDED-ADDITION FUZZY SPLICING SYSTEMS AND THEIR VARIANTS

A splicing system is one of the early theoretical proposals of the DNA-based computation device. The splicing operation starts when two DNA molecules are cut at specific subsequences with the presence of restriction enzymes: the first part is then connected to the second part of the other molecule, or vice versa, to produce splicing languages. Fuzzy with bounded-addition operation has been introduced as a restriction in splicing systems to increase the generative power of the languages generated. In this research, a graphical user interface is developed to generate all the splicing languages generated by bounded-addition fuzzy splicing systems and their variants. An algorithm is developed using JAVA and Visual Studio Code software in order to replace the time-consuming manual computation of the languages generated by bounded-addition fuzzy DNA splicing systems and their variants