Yee Siang Gan

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 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 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.

Magic star puzzle for educational mathematics

One of the interesting fields in recreational mathematics is the magic number arrangement. There are different kinds of arrays in the arrangement for a group of numbers. In particular, one of the arrays in magic number arrangement is called magic star. In fact, magic star involves combinatorics that contributes to geometrical analysis and number theory. Hence, magic star is suitable to be introduced as educational mathematics to cultivate interest in different area of mathematics. To obtain the solutions of normal magic stars of order six, the possible sets of numbers for every line in a magic star have been considered. Previously, the calculation for obtaining the solutions has been done manually which is time-consuming. Therefore, a programming code to generate all the fundamental solutions for normal magic star of order six without including the properties of rotation and reflection has been done. In this puzzle, a magic star puzzle is created by using Matlab software, which enables a user to verify the entries for the cells of magic star of order six. Moreover, it is also user-friendly as it provides interactive commands on the inputs given by the user, which enables the user to detect the incorrect inputs. In addition, user can also choose to view all the fundamental solutions as generated by the programming code.