Wan Heng Fong

Universiti Teknologi Malaysia | UTM · Department of Mathematical Sciences, Faculty of Science

In 1987, Head [1] proposed a splicing method as a mathematical model for DNA recombination. In this model, two DNA molecules are cut at specific recognition sites, and the prefix of one molecule is combined with the suffix of the other, creating a new string. Splicing operations in the system are represented as splicing rules, formalizing the proce...

In formal language theory, parallel rewriting systems have been extensively studied since its introduction in 1968 by Lindenmayer. Since their early application in mathematical biology, L-systems have solidified their position in the field of DNA computing as the parallel alternative to Chomsky grammars. On the other hand, bonded systems have also...

Concepts in graph theory are widely applied in various fields, where graphs are used to describe problems in order to give methods of solutions. In DNA computing, the complexity of DNA splicing process has led to the study on graph splicing system. Basically, a graph splicing system is introduced to illustrate three dimensional DNA splicing process...

The field of formal language theory involves the construction of words or sentences through a meticulous framework called a system. The set of words derived from the same system is called a language, where it is readily capable of undergoing set operations such as union, concatenation, concatenation closure, -free concatenation closure, homomorphi...

Through the years, formal language theory has evolved through continual interdisciplinary work in theoretical computer science, discrete mathematics and molecular biology. The combination of these areas resulted in the birth of DNA computing. Here, language generating devices that usually considered any set of letters have taken on extra restrictio...

Graph splicing system is a notion originally used to illustrate the one-dimensional string of DNA splicing in the form of a graph. A graph splicing system is associated with a graph splicing scheme where graph splicing rules are defined. A graph splicing rule restricts the possible cuts to occur on the edges of the initial graph(s) in a graph splic...

DNA splicing system is initiated by Head to mathematically model a relation between formal language theory and DNA molecules. In DNA splicing systems, DNA molecules are cut and recombined in specific ways with the existence of enzymes, which are also known as endonucleases, to produce further molecules. The resulting molecules are depicted as splic...

Splicing system was introduced by Head in 1987 in order to explore the recombinant behaviour of deoxyribonucleic acid (DNA) strands in the presence of restriction enzymes and ligases. Restriction enzymes cut the DNA strands into a left - pattern and right-pattern while the ligases recombine the left-pattern of the first string with the right-patter...

Head in 1987 was the first person to introduce the concept of splicing system as a theoretical model for DNA based computation using splicing operation. Splicing operation is a method of cutting and recombining DNA molecules under the influence of restriction enzymes such as ligase. Previous researches have proven that splicing systems with finite...

The mathematical modelling of DNA splicing systems is developed from the biological process of recombinant DNA where DNA molecules are cut and reassociated with the presence of a ligase and restriction enzymes. The molecules resulting from the splicing system generate a language which is known as a splicing language using formal language theory. In...

In biology, DNA splicing system models the recombination behaviours of DNA molecules which require the presence of restriction enzymes. Since it is quite incompetent to describe DNA splicing system in one-dimensional string, hence graph theory is used in describing the complexity of DNA splicing system. Thus by graph splicing system, a type of semi...

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, re...

In DNA computing, a sticker system is a computing mechanism involving the Watson-Crick complementarity of DNA molecules. The sticker system is known as a language generating device based on the sticker operation which is analyzed through the concept of formal language theory. The grammar of a formal language can be described by determining finite s...

The field of DNA computing has broadened the perspective of scientists since its inception. An area of interest in this field involves the combination of theoretical computer science and molecular biology. By using the concepts of string generation and molecular structure of DNA, formal language theory can be used to model the behavior of DNA molec...

Insertion-deletion systems have been extensively studied throughout the years for their powerful computational capability in the field of DNA computing. The pioneering contextual insertion-deletion system and its subsequent variants have been shown to be computationally complete, that is, they are able to generate recursively enumerable languages....

In DNA splicing system, DNA molecules are cut and recombined with the presence of restriction enzymes and a ligase. The splicing system is analysed via formal language theory where the molecules resulting from the splicing system generate a language which is called a splicing language. In nature, DNA molecules can be read in two ways; forward and b...

DNA computing, or more generally, molecular computing, is a recent development on computations using biological molecules, instead of the traditional silicon-chips. Some computational models which are based on different operations of DNA molecules have been developed by using the concept of formal language theory. The operations of DNA molecules in...

In DNA splicing systems, restriction enzymes and ligases cleave and recombine DNA molecules based on the cleavage pattern of the restriction enzymes. The set of molecules resulting from the splicing system depicts a splicing language. In this research, an algorithm for DNA splicing systems is developed using C++ visual programming. The splicing lan...

The modelling of splicing systems is simulated by the process of cleaving and recombining DNA molecules with the presence of a ligase and restriction enzymes which are biologically called as endodeoxyribonucleases. The molecules resulting from DNA splicing systems are known as splicing languages. Palindrome is a sequence of strings that reads the s...

Sticker systems and Watson-Crick automata are two modellings of DNA molecules in DNA computing. A sticker system is a computational model which is coded with single and double-stranded DNA molecules; while Watson-Crick automata is the automata counterpart of sticker system which represents the biological properties of DNA. Both of these models use...

DNA splicing system is mathematically modelled by the process of recombinant DNA which focuses on the possible reaction of sets of restriction enzymes and a ligase. The restriction enzymes are known as endodeoxyribonucleases that allow DNA molecules to be cut and reassociated. The cutting point of a restriction enzyme is determined by its cleavage...

Sticker system is a computer model which is coded with single and double-stranded molecules of DNA; meanwhile, Watson-Crick automata is the automata counterpart of the sticker system representing the biological properties of DNA. Both are the modelings of DNA molecules in DNA computing which use the feature of Watson-Crick complementarity. Formerly...

In chemistry, point group is a type of group used to describe the symmetry of molecules. It is a collection of symmetry elements controlled by a form or shape which all go through one point in space, which consists of all symmetry operations that are possible for every molecule. Next, a set of number or matrices which assigns to the elements of a g...

DNA computing, or more generally, molecular computing, is a recent development at the interface of computer science and molecular biology. In DNA computing, many computational models have been proposed in the framework of formal language theory and automata such as Watson-Crick grammars and sticker systems. A Watson-Crick grammar is a grammar model...

This research focuses on introducing one type of static Watson-Crick grammars known as static Watson-Crick linear grammars with their computational power.

A Watson-Crick Petri net is a model that enhances a Petri net with the Watson-Crick complementarity feature adapted from DNA molecules. The transitions of a Watson-Crick Petri net are labelled with pairs of symbols, and a firing sequence of transitions of the Watson-Crick Petri net is considered as successful if and only if it produces complete dou...

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 class...

In DNA splicing system, the potential effects of sets of restriction enzymes and a ligase that allow DNA molecules to be cleaved and reassociated to produce further molecules are studied. A splicing language depicts the molecules resulting from a splicing system. In this research, a C++ programming code for DNA splicing system with one palindromic...

In DNA splicing system, the potential effect of sets of restriction enzymes and a ligase that allow DNA molecules to be cleaved and re-associated to produce further molecules is modelled mathematically. This modelling is done in the framework of formal language theory, in which the nitrogen bases, nucleotides and restriction sites are modelled as a...

A place-labelled Petri net controlled grammar is, in general, a context-free grammar equipped with a Petri net and a function which maps places of the net to productions of the grammar. The languages of place-labelled Petri net controlled grammar consist of all terminal strings that can be obtained by parallel application of the rules of multisets...

Insertion is an operation in formal language theory that generalizes the operation of concatenation of words, where its variants allow the operation in different ways. Parallel insertion is a variant of insertion that simultaneously adds words between all letters of a word and also at the right and left extremities. In previous research, restrictio...

The operation of insertion has been studied extensively throughout the years for its impact in many areas of theoreticalcomputer science such as DNAcomputing. 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 place-labelled Petri net (pPN) controlled grammar is a context-free grammar equipped with a Petri net and a function which maps places of the net to the productions of the grammar. The language consists of all terminal strings that can be obtained by simultaneously applying the rules of multisets which are the images of the sets of the input plac...

Sticker systems have been introduced as a type of DNA computing model by using the recombination behaviour of DNA molecules. The systems use the Watson-Crick complementary principle of DNA molecules to perform the computation in generating new strings. By associating some weights to the axioms and dominoes of the sticker system, a new version of re...

We introduce a new variant of insertion systems, namely bonded insertion systems. In such systems, words are not only formed by usual letters but also by bonds between letters. Words which can be inserted, have " free " bonds at their ends which control at which positions in a word they can be inserted (namely only there, where the bonds " fit ")....

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 u...

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 syst...

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...

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 gram...

A splicing system involves the process of cutting and pasting on DNA molecules with the presence of restriction enzymes and ligase, respectively. A mathematical model of the splicing system has been developed by using the concept of formal language theory, which is a branch of theoretical computer science and applied discrete mathematics, and infor...

The pioneer model of deoxyribonucleic acid (DNA) splicing system in a framework of Formal Language Theory was introduced by Head that led to the existence of other models of splicing system, namely Paun, Pixton and Yusof-Goode. These entire models are inspired by the molecular biological process of DNA splicing. Hence, this paper focuses on the tra...

The concept of probabilistic splicing system was introduced as a model for stochastic processes using DNA computing techniques. In this paper we introduce splicing systems endowed with different continuous and discrete probabilistic distributions and call them as probabilistic splicing systems. We show that any continuous distribution does not incr...

Sticker system has been introduced in 1994 as a model for DNA computing using the re-combination behaviour of DNA molecules. A sticker model is an abstract computational model which uses the Watson-Crick complementarity principle of DNA molecules. Starting from the incomplete double-stranded sequences, and by iterative sticking operations, complete...

Splicing system, which is an abstraction of operations on DNA molecules, can be modelled mathematically under the framework of formal language theory and informational macromolecules. The recombinant behavior of the set of double-stranded DNA molecules under the influence of restriction enzyme and ligase further lead to the cut and paste phenomenon...

DNA splicing process is a study on the recombinant behavior of double-stranded DNA molecules with the existence of restriction enzyme and ligase. Head introduced the first mathematical model of splicing systems by using the relation of informational macromolecules and formal language theory. In addition, a few laboratory experiments have been condu...

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...

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 a...

In this paper we introduce a new variant of splicing systems, called fuzzy splicing systems, and establish some basic properties of lan-guage families generated by this type of splicing systems. We study the "fuzzy effect" on splicing operations, and show that the "fuzzification" of splicing systems can increase and decrease the computational power...

Watson-Crick automata are one of the automata types that are used for transitions with two reading heads. This automata work on double stranded sequences related by a complementarity relation similar with the Watson-Crick complementarity of DNA molecules. Watson-Crick automata can be related to a Petri net, which is a graphical and mathematical for...

The investigation on the behavior of deoxyribonucleic acid (DNA) splicing languages has been of interest of many biologists and mathematicians. Yusof-Goode (Y-G) splicing system has been introduced for the purpose of showing the transparent biological process of DNA splicing systems. In this paper, the approach of Y-G splicing system is applied in...

A Watson-Crick automaton is an automaton that works on tapes which are double stranded sequences of symbols related by Watson-Crick complementarity that are similar to the DNA molecules. However, this automaton cannot exploit the other fundamental features of DNA molecules such as the massive parallelism. Watson-Crick automata can be related to a m...

A model for DNA computing using the recombination behaviour of DNA molecules known as a sticker system has been introduced by Adleman in 1994. A sticker model is an abstract computational model which uses the Watson-Crick complementary principle of DNA molecules. Starting from the axioms – incomplete double stranded sequences, and iteratively using...

A Watson-Crick Petri net is a new formal model that enhances a Petri net with the Watson-Crick complementary feature adapted from DNA molecules. The transitions of a Watson-Crick Petri net are labeled with pairs of symbols, and a firing sequence of transitions of the Watson-Crick Petri net is considered as successful if and only if it produces comp...

Sticker systems were introduced in 1998 as one of the DNA computing models by using the recombination behavior of DNA molecules. The Watson-Crick complementary principle of DNA molecules is abstractly used in the sticker systems to perform the computation of sticker systems. In this paper, the generative power of weighted one-sided sticker systems...

Recently, the relation of automata and groups has been studied. It was shown that properties of groups can be studied using state diagrams of modified automata and modified Watson-Crick automata. In this work, we investigate the relation of subgroups with the modified finite and Watson-Crick automata. We also establish the conditions for the recogn...

The concepts of splicing system involve the study of cut and paste phenomenon of deoxyribonucleic acid (DNA). The splicing language, which is resulted from a splicing system, can be classified as inert persistent language, active persistent language and limit language. As one of the types of splicing language, limit language can biologically be ref...

A weighted splicing system is a restriction of splicing systems in which weights are associated with the axioms, and the weight of a string z generated from two strings x and y is computed from the weights of x and y according to some operations defined on the weights. In this paper we study the computational power of weighted splicing systems cons...

A splicing system, one of the early theoretical models for DNA computing was introduced by Head in 1987. Splicing systems are based on the splicing operation which, informally, cuts two strings of DNA molecules at the specific recognition sites and attaches the prefix of the first string to the suffix of the second string, and the prefix of the sec...

Sticker systems have been introduced by Kari in 1998as an abstract computational model which uses the Watson-Crick complementary principle of DNA molecules: starting from the incomplete double stranded sequences and iteratively using sticking operations, complete double stranded sequences are obtained. It is known that sticker systems with finite s...

DNA computing has been widely developed after the Hamiltonian path problems have been solved using DNA molecules as computational tools in test tubes [1]. New types of bio-computer are then theoretically proposed to replace the primitive binary systems based computer. Moreover, the operation of this new type of bio-computer is based on DNA computin...

The study on cutting and pasting of DNA molecules under the framework of Formal Language Theory has led to the mathematical modelling of splicing system. The output of splicing system is the splicing language which can be categorized into three types: adult or inert persistent, transient and limit language. In the biological point of view, limit la...

The cutting and pasting processes that occur in DNA molecules have led to the formulation of splicing system. Since then, there are few models used to model the splicing system. The splicing language, which is the product of splicing system, can be categorized into two, namely the adult and limit language. In this research, limit language is extend...

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. Splicing systems with finite sets of axioms only generate regular languages. Hence, different restrictions have been considered to increase the computational power up to the recursively enumer...

Splicing system which is a mathematical model that describes splicing (cutting) and recombinant (pasting) behaviors was introduced by Head in 1987. Since then many researches came out with new ideas regarding splicing system that was analyzed under the formal language theory. These include simple and semi simple splicing system. The idea of non sem...

A theoretical model for DNA computing using the recombination behavior of DNA molecules known as asplicing system has been introduced in 1987. Splicing systems are based on the splicing operation which, informally, cuts two strings at the specific places and attaches the prefix of the first string to the suffix of the second string and the prefix o...

Splicing system is known as a mathematical model that initiates the connection between the study of DNA molecules and formal language theory. In splicing systems, languages called splicing languages refer to the set of double-stranded DNA molecules that may arise from an initial set of DNA molecules in the presence of restriction enzymes and ligase...

A finite automaton is one of the classic models of recognition devices, which is used to determine the type of language a string belongs to. A string is said to be recognized by a finite automaton if the automaton "reads" the string from the left to the right starting from the initial state and finishing at a final state. Another type of automata w...

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 th...

In this paper we introduce splicing systems with probabili-ties, 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.

Automata act as classical models for recognition devices. From the previous researches, the classical models of automata have been used to scan strings and to determine the types of languages a string belongs to. In the study of automata and group theory, it has been found that the properties of a group can be recognized by the automata using the a...

Sticker systems were first introduced as a language generating device based on the operation of sticking. A new molecule is produced from the starting axiom, which is prolonged to the left or to the right using given single stranded strings or dominoes. For each sticker operation, an element of a group (called valence) will be associated with the a...

DNA computing is an emerging field that includes the combination of some concepts from biology and computation. Splicing system is a mathematical model in DNA computing which was first introduced by Head in 1987. This model is defined under the framework of formal language theory which is a subcategory of theoretical computer science and applied di...

Sticker system has been introduced by Kari in 1998 as a model for DNA computing using the recombination behaviour of DNA molecules. A sticker model is an abstract computational model which uses the Watson-Crick complementary principle of DNA molecules.A sticker operation works by using ligation and annealing operation to form a complete double stra...

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 carrie...

A model for DNAcomputing using the recombination behavior of DNA molecules, known as a sticker system, was introduced by by L. Kari, G. Paun, G. Rozenberg, A. Salomaa, and S. Yu in the paper entitled DNAcomputing, sticker systems and universality from the journal of Acta Informatica vol. 35, pp. 401-420 in the year 1998. A sticker system uses the W...

One of the classic models of automata is finite automata, which determine whether a string belongs to a particular language or not. The string accepted by automata is said to be recognized by that automata. Another type of automata, so-called Watson-Crick automata, with two reading heads that work on double-stranded tapes using the complimentary re...

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.

A Head splicing system (H-system)consists of a finite set of strings (words) written over a finite alphabet, along with a finite set of rules that acts on the strings by iterated cutting and pasting to create a splicing language. Any interpretation that is aligned with Tom Head's original idea is one in which the strings represent double-stranded d...