Sticker Systems Research Articles

On the Languages Accepted by Watson-Crick Finite Automata with Delays

In this work, we analyze the computational power of Watson-Crick finite automata (WKFA) if some restrictions over the transition function in the model are imposed. We consider that the restrictions imposed refer to the maximum length difference between the two input strands which is called the delay. We prove that the language class accepted by WKFA with such restrictions is a proper subclass of the languages accepted by arbitrary WKFA in general. In addition, we initiate the study of the language classes characterized by WKFAs with bounded delays. We prove some of the results by means of various relationships between WKFA and sticker systems.

Static Watson-Crick Linear Grammars and Its Computational Power

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 inspire various types of formal language tools which include sticker systems, grammars and automata. Recently, the grammar counterparts of Watson-Crick automata known as Watson-Crick grammars which consist of regular, linear and context-free grammars, are defined as grammar models that generate double-stranded strings using the important feature of Watson-Crick complementarity rule. In this research, a new variant of static Watson-Crick linear grammar is introduced as an extension of static Watson-Crick regular grammar. A static Watson-Crick linear grammar is a grammar counterpart of sticker system that generates the double-stranded strings and uses rule as in linear grammar. The main result of the paper is to determine some computational properties of static Watson-Crick linear grammars. Next, the hierarchy between static Watson-Crick languages, Watson-Crick languages, Chomsky languages and families of languages generated by sticker systems are presented.

Static Watson-Crick Context-Free Grammars

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 the feature of Watson-Crick complementarity in DNA computing. Previously, the grammar counterpart of the Watson-Crick automata have been introduced, known as Watson-Crick grammars which are classified into three classes: Watson-Crick regular grammars, Watson-Crick linear grammars and Watson-Crick context-free grammars. In this research, a new variant of Watson-Crick grammar called a static Watson-Crick context-free grammar, which is a grammar counterpart of sticker systems that generates the double-stranded strings and uses rule as in context-free grammar, is introduced. The static Watson-Crick context-free grammar differs from a dynamic Watson-Crick context-free grammar in generating double-stranded strings, as well as for regular and linear grammars. The main result of the paper is to determine the generative powers of static Watson-Crick context-free grammars. Besides, the relationship of the families of languages generated by Chomsky grammars, sticker systems and Watson-Crick grammars are presented in terms of their hierarchy.

Computational Power of Static Watson-Crick Context-free Grammars

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, Watson-Crick grammars which are classified into three classes have been introduced [1]. In this research, a grammar counterpart of sticker systems that uses the rule as in context-free grammar is introduced, known as a static Watson-Crick context-free grammar. The research finding on the computational power of these grammar shows that the family of context-free languages is strictly included in the family of static Watson-Crick context-free languages; the static Watson-Crick context-free grammars can generate non context-free languages; the family of Watson-Crick context-free languages is included in the family of static Watson-Crick context-free languages which are presented in terms of their hierarchy.

Static Watson-Crick regular grammar

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 that generates double stranded strings, whereas a sticker system is a DNA computing model of the ligation and annealing operations over DNA strands using the Watson-Crick complementarity to form a complete double stranded DNA sequence. Most of the proposed DNA computing models make use of this concept, including the Watson-Crick grammars and sticker systems. Watson-Crick grammars and their variants can be explored using formal language theory which allows the development of new concepts of Watson-Crick grammars. In this research, a new variant of Watson-Crick grammar called a static Watson-Crick regular grammar is introduced as an analytical counterpart of sticker systems. The computation of a sticker system starts from a given set of incomplete double stranded sequence to form a complete double stranded sequence. Here, a static Watson-Crick regular grammar differs from a dynamic Watson-Crick regular grammar in generating double stranded strings: the latter grammar produces each strand string “independently” and only check for the Watson-Crick complementarity of a generated complete double stranded string at the end, while the former grammar generates both strand strings “dependently”, i.e., checking for the Watson-Crick complementarity for each complete substring. In this paper, computational properties of static Watson-Crick regular grammars are investigated to correlate with the Chomsky hierarchy and hierarchy of the families of dynamic Watson-Crick regular languages. The relationship between families of languages generated by static Watson-Crick regular grammars with several variants of sticker systems, Watson-Crick regular grammars and Chomsky grammars are presented by showing the hierarchy.

Variants of weighted sticker systems with different weighting spaces

Sticker systems have been introduced as one of the DNA computing models by using the recombination behavior of DNA molecules in 1998. Abstractly, 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 sticker system, a new version of restricted sticker system namely weighted sticker system has been introduced. In this paper, we study the generative power of weighted sticker systems by considering the languages generated by weighted sticker system with different weighting spaces and cut-points. The relations of the languages generated by weighted sticker systems in the Chomsky hierarchy are also investigated.

Generative capacity of sticker systems with the presence of weights

DNA computing involves computing models which use the recombination behavior of DNA molecules as computation devices. This idea was successfully applied by Adleman in his biological experiment in order to show the solvability of the Hamiltonian path problem for larger instances. In 1998, a DNA based computation model, called sticker system, which is an abstraction of the computations using the recombination behavior as in Adleman’s experiment was proposed. In 2013, a new variant of sticker system using weights was introduced, namely the weighted sticker system. In this paper, the generative capacity for several variants of bounded delay and nonrestrictive weighted sticker systems are investigated. The relation between families of languages generated by several variants of weighted sticker systems and weighted grammars are also presented.

Sticker Systems Over Monoids

Molecular computing has gained many interests among researchers since Head introduced the first theoretical model for DNA based computation using the splicing operation in 1987. Another model for DNA computing was proposed by using the sticker operation which Adlemanused in his successful experiment for the computation of Hamiltonian paths in a graph: a double stranded DNA sequence is composed by prolonging to the left and to the right a sequence of (single or double) symbols by using given single stranded strings or even more complex dominoes with sticky ends, gluing these ends together with the sticky ends of the current sequence according to a complementarity relation. According to this sticker operation, a language generative mechanism, called a sticker system, can be defined: a set of (incomplete) double-stranded sequences (axioms) and a set of pairs of single or double-stranded complementary sequences are given. The initial sequences are prolonged to the left and to the right by using sequences from the latter set, respectively. The iterations of these prolongations produce “computations” of possibly arbitrary length. These processes stop when a complete double stranded sequence is obtained. Sticker systems will generate only regular languages without restrictions. Additional restrictions can be imposed on the matching pairs of strands to obtain more powerful languages. Several types of sticker systems are shown to have the same power as regular grammars; one type is found to represent all linear languages whereas another one is proved to be able to represent any recursively enumerable language. The main aim of this research is to introduce and study sticker systems over monoids in which with each sticker operation, an element of a monoid is associated and a complete double stranded sequence is considered to be valid if the computation of the associated elements of the monoid produces the neutral element. Moreover, the sticker system over monoids is defined in this study.

Probabilistic sticker systems

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 sticking operations, complete double stranded sequences are obtained. It is known that sticker systems with finite sets of axioms and sticker rules generate only regular languages. Hence, different types of restrictions have been considered to increase the computational power of sticker systems. In this paper, we introduce probabilistic sticker systems in which probabilities are initially associated with the axioms, and the probability of the generated string is computed by multiplying the probabilities of all occurrences of the initial strings used in the computation of the string.

Spatial Cluster Analysis by the Bin-Packing Problem and DNA Computing Technique

Spatial cluster analysis is an important data mining task. Typical techniques include CLARANS, density- and gravity-based clustering, and other algorithms based on traditional von Neumann's computing architecture. The purpose of this paper is to propose a technique for spatial cluster analysis based on sticker systems of DNA computing. We will adopt the Bin-Packing Problem idea and then design algorithms of sticker programming. The proposed technique has a better time complexity. In the case when only the intracluster dissimilarity is taken into account, this time complexity is polynomial in the amount of data points, which reduces the NP-completeness nature of spatial cluster analysis. The new technique provides an alternative method for traditional cluster analysis.

Sticker P System

A computability model based on DNA sequences called sticker systems was introduced by Kari et al. (1998). Sticker systems are language generating devices based on the sticker operation. In this work, a theoretical study about a new class of P system based on the sticker operation has been proposed. In this system, objects are double stranded sequences with sticky ends and evolution rules are sticking rules based on sticker operation. The authors compare the language generated by the proposed system with regular languages. The authors suggest another P system based on the bidirectional sticker system.

Computing by observing: Simple systems and simple observers

We survey and extend the work on the paradigm called “computing by observing”. Its central feature is that one considers the behavior of an evolving system as the result of a computation. To this purpose an external observer records this behavior. In this way, several computational trade-offs between the observer and the observed system can be determined. It has turned out that the observed behavior of computationally simple systems can be very complex, when an appropriate observer is used. For example, a restricted version of context-free grammars with regular observers suffices to obtain computational completeness. As a second instantiation presented here, we apply an observer to sticker systems, an abstract model of DNA computing. Finally, we introduce and investigate the case where the observers can read only one measure of the observed system (e.g., mass or temperature), modeling in this way the limitations in the observation of real physical systems. Finally, a research perspective on the topic is presented.

Analysis for Graph Coloring Problem Based on Sticker and Deletion Systems

Graph coloring problem is a NP-complete one of graph and combinatorial optimization.The computational time increases exponentially with the size of the researched problem solved using the usual methods.Thus it is impossible to settle it efficiently.Sticker system and deletion system are the language generated mechanisms based on sticking and deleting operations respectively.In this paper,graph coloring problem was combined with the number of bad edges and transformed into a problem of searching for the longest sequence.On the basis,the chromatic number and all the color classes of graph were obtained using the parallelism of two formal models:sticker system and deletion system.Compared with the existing DNA algorithm for graph coloring problem,the proposed algorithm is of lower complexity.

Complexity through the Observation of Simple Systems

We survey work on the paradigm called "computing by observing." Its central feature is that one considers the behavior of an evolving system as the result of a computation. To this end an observer records this behavior. It has turned out that the observed behavior of computationally simple systems can be very complex, when an appropriate observer is used. For example, a restricted version of context-free grammars with regular observers suffices to obtain computational completeness. As a second instantiation presented here, we apply an observer to sticker systems. Finally, some directions for further research are proposed.

On the power of parallel communicating Watson–Crick automata systems

Parallel communicating Watson–Crick automata systems were introduced in [E. Czeizler, E. Czeizler, Parallel communicating Watson–Crick automata systems, in: Z. Ésik, Z. Fülöp (Eds.), Proc. Automata and Formal Languages, Dobogókő, Hungary, 2005, pp. 83–96] as possible models of DNA computations. This combination of Watson–Crick automata and parallel communicating systems comes as a natural extension due to the new developments in DNA manipulation techniques. It is already known, see [D. Kuske, P. Weigel, The Role of the Complementarity Relation in Watson–Crick Automata and Sticker Systems, DLT 2004, Lecture Notes in Computer Science, Vol. 3340, Auckland, New Zealand, 2004, pp. 272–283], that for Watson–Crick finite automata, the complementarity relation plays no active role. However, this is not the case when considering parallel communicating Watson–Crick automata systems. In this paper we prove that non-injective complementarity relations increase the accepting power of these systems. We also prove that although Watson–Crick automata are equivalent to two-head finite automata, this equivalence is not preserved when comparing parallel communicating Watson–Crick automata systems and multi-head finite automata.

Sticker systems with complex structures

In this paper, we propose a variant of sticker systems which uses molecules with complex structures. Since the original sticker systems (Paun et al. (1998) [2, 8]) working on double strands of DNA have been studied as a formal model for self-assembly in DNA computing, we extend the sticker systems to working on more complex (higher-order) structures of DNA molecules. The advantage of sticker systems with complex structures is that augmented with weak codings we can obtain the characterization of recursively enumerable languages by using only sticking (hybridization) operations for complex molecules, while the usual sticker systems require more complicated operations such as the simultaneous use of couples of dominoes or coherent computations besides morphisms.

Sticker systems

Sticker systems is a computational model which is an abstraction of the way that the Watson-Crick complementarity is used in DNA computing. We consider such systems of a general form, with blocks of arbitrary shapes to be annealed to the currently built sequences. We investigate the generative power of several variants of sticker systems. Characterizations of regular, linear, and recursively enumerable languages are obtained in this framework.

DNA computing, sticker systems, and universality

We introduce the sticker systems, a computability model, which is an abstraction of the computations using the Watson-Crick complementarity as in Adleman's DNA computing experiment, [1]. Several types of sticker systems are shown to characterize (modulo a weak coding) the regular languages, hence the power of finite automata. One variant is proven to be equivalent to Turing machines. Another one is found to have a strictly intermediate power.