DNA splicing: computing by observing

Motivated by several techniques for observing molecular processes in real-time we introduce a computing device that stresses the role of the observer in biological computations and that is based on the observed behavior of a splicing system. The basic idea is to introduce a marked DNA strand into a test tube with other DNA strands and restriction enzymes. Under the action of these enzymes the DNA starts to splice. An external observer monitors and registers the evolution of the marked DNA strand. The input marked DNA strand is then accepted if its observed evolution follows a certain expected pattern. We prove that using simple observers (finite automata), applied on finite splicing systems (finite set of rules and finite set of axioms), the class of recursively enumerable languages can be recognized. © Springer Science+Business Media B.V. 2007

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

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

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

P Systems and Topology: Some Suggestions for Research

Lately, some studies linked the computational power of abstract computing systems based on multiset rewriting to Petri nets and the computation power of these nets to their topology. In turn, the computational power of these abstract computing devices can be understood just looking at their topology, that is, information flow. This line of research is very promising for several aspects: its results are valid for a broad range of systems based on multiset rewriting; it allows to know the computational power of abstract computing devices without tedious proofs based on simulations; it links computational power to topology and, in this way, it opens a broad range of questions. In this note we summarize the known result on this topic and we list a few suggestions for research together with the relevance of possible outcomes

Computing with Spiking Neural P Systems: Traces and Small Universal Systems

Recently, the idea of spiking neurons and thus of computing by spiking was incorporated into membrane computing, and so-called spiking neural P systems (abbreviated SN P systems) were introduced. Very shortly, in these systems neurons linked by synapses communicate by exchanging identical signals (spikes), with the information encoded in the distance between consecutive spikes. Several ways of using such devices for computing were considered in a series of papers, with universality results obtained in the case of computing numbers, both in the generating and the accepting mode; generating, accepting, or processing strings or infinite sequences was also proved to be of interest. In the present paper, after a short survey of central notions and results related to spiking neural P systems (including the case when SN P systems are used as string generators), we contribute to this area with two (types of) results: (i) we produce small universal spiking neural P systems (84 neurons are sufficient in the basic definition, but this number is decreased to 49 neurons if a slight generalization of spiking rules is adopted), and (ii) we investigate the possibility of generating a language by following the trace of a designated spike in its way through the neurons.Ministerio de Educación y Ciencia TIN2005-09345-C03-0

Accepting splicing systems with permitting and forbidding words

Abstract: In this paper we propose a generalization of the accepting splicingsystems introduced in Mitrana et al. (Theor Comput Sci 411:2414?2422,2010). More precisely, the input word is accepted as soon as a permittingword is obtained provided that no forbidding word has been obtained sofar, otherwise it is rejected. Note that in the new variant of acceptingsplicing system the input word is rejected if either no permitting word isever generated (like in Mitrana et al. in Theor Comput Sci 411:2414?2422,2010) or a forbidding word has been generated and no permitting wordhad been generated before. We investigate the computational power ofthe new variants of accepting splicing systems and the interrelationshipsamong them. We show that the new condition strictly increases thecomputational power of accepting splicing systems. Although there areregular languages that cannot be accepted by any of the splicing systemsconsidered here, the new variants can accept non-regular and even non-context-free languages, a situation that is not very common in the case of(extended) finite splicing systems without additional restrictions. We alsoshow that the smallest class of languages out of the four classes definedby accepting splicing systems is strictly included in the class of context-free languages. Solutions to a few decidability problems are immediatelyderived from the proof of this result

An Observer-Based De-Quantisation of Deutsch’s Algorithm

Deutsch’s problem is the simplest and most frequently examined example of computational problem used to demonstrate the superiority of quantum computing over classical computing. Deutsch’s quantum algorithm has been claimed to be faster than any classical ones solving the same problem, only to be discovered later that this was not the case. Various dequantised solutions for Deutsch’s quantum algorithm—classical solutions which are as efficient as the quantum one—have been proposed in the literature. These solutions are based on the possibility of classically simulating “superpositions”, a key ingredient of quantum algorithms, in particular, Deutsch’s algorithm. The de-quantisation proposed in this note is based on a classical simulation of the quantum measurement achieved with a model of observed system. As in some previous dequantisations of Deutsch’s quantum algorithm, the resulting dequantised algorithm is deterministic. Finally, we classify observers (as finite state automata) that can solve the problem in terms of their “observational power”