Wan Heng Fong

Probabilistic Splicing Systems

In this paper we introduce splicing systems with probabilities, i.e., probabilistic splicing systems, and establish basic properties of language families generated by this type of splicing systems. We show that a simple extension of splicing systems with probabilities may increase the computational power of splicing systems with finite components.

An analysis of four variants of splicing system

The theoretical development of splicing system has led to the formulation of new extension of splicing system, namely Yusof-Goode (Y-G) splicing system. This Y-G splicing system, which is associated with Y-G splicing rule, is introduced to show the transparent biological process of DNA splicing. In this paper, a theoretical analysis has been carried out to investigate the similarities and differences between Y-G splicing system with the existing splicing systems namely, Head, Paun and Pixton splicing system in biological point of view.

Weighted splicing systems

In this paper we introduce a new variant of splicing systems, called weighted splicing systems, and establish some basic properties of language families generated by this type of splicing systems. We show that a simple extension of splicing systems with weights can increase the computational power of splicing systems with finite components.

The conjugacy classes and conjugacy class graphs of point groups of order at most 8

In group theory, conjugacy class is a method of partitioning the elements of a group such that the elements a and b are conjugate in a group G if xax−1 = b for some x in G. Meanwhile, a point group is a set of symmetry operations that keeps at least one point in a molecule fixed. In chemistry, symmetry of molecules is important since chemists classify molecules based on their symmetry. In this research, the conjugacy classes of point groups of order at most eight are computed. The conjugacy classes of these groups are then applied to graph theory to obtain the conjugacy class graph, which is a graph whose vertices V = (v1,…,vn) are the non-central conjugacy classes of a group and the two vertices are connected if their cardinalities are not coprime, that is the greatest common divisor of the cardinalities of the corresponding vertices is not equal to one.In group theory, conjugacy class is a method of partitioning the elements of a group such that the elements a and b are conjugate in a group G if xax−1 = b for some x in G. Meanwhile, a point group is a set of symmetry operations that keeps at least one point in a molecule fixed. In chemistry, symmetry of molecules is important since chemists classify molecules based on their symmetry. In this research, the conjugacy classes of point groups of order at most eight are computed. The conjugacy classes of these groups are then applied to graph theory to obtain the conjugacy class graph, which is a graph whose vertices V = (v1,…,vn) are the non-central conjugacy classes of a group and the two vertices are connected if their cardinalities are not coprime, that is the greatest common divisor of the cardinalities of the corresponding vertices is not equal to one.

Generating finite cyclic and dihedral groups using sequential insertion systems with interactions

The operation of insertion has been studied extensively throughout the years for its impact in many areas of theoretical computer science such as DNA computing. First introduced as a generalization of the concatenation operation, many variants of insertion have been introduced, each with their own computational properties. In this paper, we introduce a new variant that enables the generation of some special types of groups called sequential insertion systems with interactions. We show that these new systems are able to generate all finite cyclic and dihedral groups.

The generative capacity of weighted simple and semi-simple splicing systems

The mathematical modelling of splicing systems (H systems) was initiated by Head in 1987. By restricting the splicing rules of splicing systems, some variants of splicing systems such as simple and semi-simple splicing systems have been developed. Due to the limitation on the generative power of the variants of splicing systems, weights have been used as the restrictions in the variants of splicing systems recently, namely weighted one-sided splicing systems, weighted simple splicing systems and weighted semi-simple splicing systems. In this paper, we investigate the generative power of weighted simple and semi-simple splicing systems by considering different and specified weighting spaces and weighting operations. In addition, the generative power of weighted simple and semi-simple splicing systems are generalised by relating their generated threshold languages to the Chomsky hierarchy.

Some restrictions on the existence of second order limit language

The cut and paste phenomenon on DNA molecules with the presence of restriction enzyme and appropriate ligase has led to the formalism of mathematical modelling of splicing system. A type of splicing system named Yusof-Goode splicing system is used to present the transparent behaviour of the DNA splicing process. The limit language that is defined as the leftover molecules after the system reaches its equilibrium point has been extended to a second order limit language. The non-existence of the second order limit language biologically has lead to this study by using mathematical approach. In this paper, the factors that restrict the formation of the second order limit language are discussed and are presented as lemmas and theorem using Y-G approach. In addition, the discussion focuses on Yusof- Goode splicing system with at most two initial strings and two rules with one cutting site and palindromic crossing site and recognition sites.

Some characteristics on the generative power of weighted one-sided splicing systems

A splicing system is a formal model for DNA based computation using the recombinant behavior of DNA molecules in the presence of enzymes and ligase. Since it was introduced in 1987, several variants with different restrictions and extensions have been developed. In this paper, a restricted variant of splicing systems, called one-sided splicing systems have been studied. The generative capacity of one-sided splicing systems with the presence of weight is investigated. We have also shown that the use of different weighting spaces and weight operations results in weighted one-sided splicing systems with different generative capacities.

The properties of probabilistic simple regular sticker system

A mathematical model for DNA computing using the recombination behavior of DNA molecules, known as a sticker system, has been introduced in 1998. In sticker system, the sticker operation is based on the Watson-Crick complementary feature of DNA molecules. The computation of sticker system starts from an incomplete double-stranded sequence. Then by iterative sticking operations, a complete double-stranded sequence is obtained. It is known that sticker systems with finite sets of axioms and sticker rule (including the simple regular sticker system) generate only regular languages. Hence, different types of restrictions have been considered to increase the computational power of the languages generated by the sticker systems. In this paper, we study the properties of probabilistic simple regular sticker systems. In this variant of sticker system, probabilities are associated with the axioms, and the probability of a generated string is computed by multiplying the probabilities of all occurrences of the initial strings. The language are selected according to some probabilistic requirements. We prove that the probabilistic enhancement increases the computational power of simple regular sticker systems.

A new variant of Petri net controlled grammars

A Petri net controlled grammar is a Petri net with respect to a context-free grammar where the successful derivations of the grammar can be simulated using the occurrence sequences of the net. In this paper, we introduce a new variant of Petri net controlled grammars, called a place-labeled Petri net controlled grammar, which is a context-free grammar equipped with a Petri net and a function which maps places of the net to productions of the grammar. The language consists of all terminal strings that can be obtained by parallelly applying multisets of the rules which are the images of the sets of the input places of transitions in a successful occurrence sequence of the Petri net. We study the effect of the different labeling strategies to the computational power and establish lower and upper bounds for the generative capacity of place-labeled Petri net controlled grammars.