We introduce a new computability model, of a distributed parallel type, based on the notion of a membrane structure. Such a structure consists of several cell-like membranes, recurrently placed inside a unique "skin" membrane. A plane representation is a Venn diagram without intersected sets and with a unique superset. In the regions delimited by the membranes there are placed objects; the obtained construct is called a super-cell. These objects are assumed to evolve: each object can be transformed in other objects, can pas through a membrane, or can disolve the membrane in which it is placed. A priority relation between evolution rules can be considered. The evolution is done in parallel for all objects able to evolve. In this way, we obtain a computing device (we call it a super-cell system): start with a certain number of objects in a certain membrane and let the system evolve; if it will halt (no object can further evolve), then the computation is finished, with the result given as...

How can molecules compute? In his early studies of reversible computation, Bennett imagined an enzymatic Turing Machine which modified a hetero-polymer (such as DNA) to perform computation with asymptotically low energy expenditures. Adleman's recent experimental demonstration of a DNA computation, using an entirely different approach, has led to a wealth of ideas for how to build DNA-based computers in the laboratory, whose energy efficiency, information density, and parallelism may have potential to surpass conventional electronic computers for some purposes. In this thesis, I examine one mechanism used in all designs for DNA-based computer -- the self-assembly of DNA by hybridization and formation of the double helix -- and show that this mechanism alone in theory can perform universal computation. To do so, I borrow an important result in the mathematical theory of tiling: Wang showed how jigsaw-shaped tiles can be designed to simulate the operation of any Turing Machine. I propose...

Biomolecular Computation(BMC) is computation at the molecular scale, using biotechnology engineering techniques. Most proposed methods for BMC used distributed (molecular) parallelism (DP); where operations are executed in parallel on large numbers of distinct molecules. BMC done exclusively by DP requires that the computation execute sequentially within any given molecule (though done in parallel for multiple molecules). In contrast, local parallelism (LP) allows operations to be executed in parallel on each given molecule. Winfree, et al [W96, WYS96]) proposed an innovative method for LP-BMC, that of computation by unmediated self-assembly of � arrays of DNA molecules, applying known domino tiling techniques (see Buchi [B62], Berger [B66], Robinson [R71], and Lewis and Papadimitriou [LP81]) in combination with the DNA self-assembly techniques of Seeman et al [SZC94]. The likelihood for successful unmediated self-assembly of computations has not been determined (we discuss a simple model of assembly where there may be blockages in self-assembly, but more sophisticated models may have a higher likelihood of success). We develop improved techniques to more fully exploit the potential power of LP-BMC. To increase

: We show how to use DNA experiments to solve the famous "SAT" problem of Computer Science. This is a special case of a more general method that can solve NP-complete problems, first introduced in [3]. The advantage of these results is the huge parallelism inherent in DNA based computing. It has the potential to yield vast speedups over conventional electronic based computers for such search problems. 1. Introduction In a recent breakthrough Adleman [1] showed how to use biological experiments to solve instances of the famous Hamiltonian Path Problem (HPP). Recall that this problem is: Given a set of "cities" and directed paths between them; Find a directed tour that starts at a given city, ends at a given city, and visits every other city exactly once. This problem (HPP) is known to be NP-complete [2]. A computational problem is in NP provided it can be formulated as a "search" problem. Further, a problem is NP-complete provided, if it has an efficient solution, then so does all of ...

Recent proposals for DNA based computing [1], [2], [3] encode Boolean vector component values with sequences of DNA. It has previously been assumed that sufficient length random subsequences could be used to encode component values. However use of such subsequences will inadvertently result in long complementary subsequences. Complementary subsequences of sufficient length would stick to each other and cause mistakes or delays in computation. We suggest some constraints on DNA subsequences to be used in encodings, and describe maximal sets of subsequences satisfying these constraints. A seminal paper of Adleman[1] recently sparked growing interest in the use of DNA and the methods of molecular biology to do computation. Adleman's approach required the encoding of computer science problems into DNA sequences, and relied heavily on "extraction" of sequences containing a particular subsequence by use of a complementary subsequence. Subsequently Lipton[2] proposed an approach for using DN...

In [Li1] and [Ad2] a formal model for molecular computing was proposed, which makes focused use of affinity purification. The use of PCR was suggested to expand the range of feasible computations, resulting in a second model. In this note, we give a precise characterization of these two models in terms of recognized computational complexity classes, namely branching programs (BP) and nondeterministic branching programs (NBP) respectively. This allows us to give upper and lower bounds on the complexity of desired computations. Examples are given of computable and uncomputable problems, given limited time. 1 Introduction Molecular computation, as introduced by [Ad1], provides a new approach to solving combinatorial inverse problems, where we are interested in computing f \Gamma1 (1) for n-bit strings x and boolean function f . Instances of NP-complete problems can be expressed in this form; for example 3-SAT. Adleman's technique involves using individual DNA strands to represent poten...

This article reviews the growing body of scientific work in Artificial Chemistry. First, common motivations and fundamental concepts are introduced. Second, current research activities are discussed along three application dimensions: modelling, information processing and optimization. Finally, common phenomena among the different systems are summarized. It is argued here that Artificial Chemistries are "the right stuff" for the study of pre-biotic and bio-chemical evolution, and they provide a productive framework for questions regarding the origin and evolution of organizations in general. Furthermore, Artificial Chemistries have a broad application range to practical problems as shown in this review.

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Recently, biochemical systems have been shown to possess interesting computational properties. In a parallel development, the chemical computation metaphor is becoming more and more frequently used as part of the emergent computation paradigm in Computer Science. We review in this contribution the idea behind the chemical computational metaphor and outline its relevance for nanotechnology. We set up a simulated reaction system of mathematical objects and examine its dynamics by computer experiments. Typical problems of computer science, like sorting, parity checking or prime number computation are placed within this context. The implications of this approach for nanotechnology, parallel computers based on molecular devices and DNA-RNA-protein information processing are discussed. 1 Introduction The idea of using natural systems for computational purposes has long been pondered. Haken, for instance, has proposed to use laser mode competition as a way to recognize patterns [1]. Others h...

In [Adl94] Adleman used biological manipulations with DNA strings to solve some instances of the Directed Hamiltonian Path Problem. Lipton [Lip94] showed how to extend this idea to solve any NP problem. We prove that exactly the problems in P NP = \Delta p 2 can be solved in polynomial time using Lipton's model. Various modifications of Lipton's model are investigated, and it is proved that their computational power in polynomial time can be characterized by one of the complexity classes P, \Delta p 2 , \Delta p 3 or even PSPACE. Restricting Liptons model to DNA strings of logarithmic length one can compute exactly the problems in L. 1 Introduction In the last years several new ideas have been developed to use non electronic natural phenomena for real, efficient computation. In classical electronic-based computations the information is stored bitwise by electric and electromagnetic means, and the information is modified by using just these properties of the memory. It is typica...