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

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

Generative capacity of sticker systems with the presence of weights

DNA computing involves computing models which use the recombination behaviour 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. A DNA-based computation model called a sticker system is an abstraction of the computations using the recombination behaviour as in Adleman’s experiment. In this paper, the generative capacity of several variants of bounded delay and unrestricted weighted sticker systems is investigated. The relation between families of languages generated by several variants of weighted sticker systems and weighted grammars is also presented

Model Checking Temporal Logic Formulas Using Sticker Automata

As an important complex problem, the temporal logic model checking problem is still far from being fully resolved under the circumstance of DNA computing, especially Computation Tree Logic (CTL), Interval Temporal Logic (ITL), and Projection Temporal Logic (PTL), because there is still a lack of approaches for DNA model checking. To address this challenge, a model checking method is proposed for checking the basic formulas in the above three temporal logic types with DNA molecules. First, one-type single-stranded DNA molecules are employed to encode the Finite State Automaton (FSA) model of the given basic formula so that a sticker automaton is obtained. On the other hand, other single-stranded DNA molecules are employed to encode the given system model so that the input strings of the sticker automaton are obtained. Next, a series of biochemical reactions are conducted between the above two types of single-stranded DNA molecules. It can then be decided whether the system satisfies the formula or not. As a result, we have developed a DNA-based approach for checking all the basic formulas of CTL, ITL, and PTL. The simulated results demonstrate the effectiveness of the new method

Using Automated Reasoning Systems on Molecular Computing

This paper is focused on the interplay between automated reasoning systems (as theoretical and formal devices to study the correctness of a program) and DNA computing (as practical devices to handle DNA strands to solve classical hard problems with laboratory techniques). To illustrate this work we have proven in the PVS proof checker, the correctness of a program, in a sticker based model for DNA computation, solving the pairwise disjoint families problem. Also we introduce the formalization of the Floyd–Hoare logic for imperative programs

Thermodynamic simulation of deoxyoligonucleotide hybridization, polymerization, and ligation

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1997.Includes bibliographical references (leaves 54-55).by Alexander J. Hartemink.M.S

Weighted sticker system

A sticker system is a computational model which uses a sticker operation on DNA molecules. A sticker operation works on the complementary relation of double stranded DNA by using ligation and annealing operation to form a complete double stranded DNA sequence. In this paper, a new variant of sticker systems, called weighted sticker systems, is introduced. Some basic properties of language families that are generated by the weighted sticker systems are investigated.This paper also introduces some restricted weighted variants of sticker systems such as weighted one-sided, regular, simple, simple one-sided and simple regular sticker systems. Moreover, the paper shows that the presence of weights increases the generative powers of usual variants of sticker systems

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

[EN] 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.This work has been developed with the financial support of the European Union's Horizon 2020 research and innovation programme under grant agreement No. 952215 corresponding to the TAILOR project.Sempere Luna, JM. (2021). On the Languages Accepted by Watson-Crick Finite Automata with Delays. Mathematics. 9(8):1-12. https://doi.org/10.3390/math9080813S1129