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We describe methods for making volume decreasing algorithms more resistant to certain types of errors. Such error recovery techniques are crucial if DNA computers ever become practical. Our first approach relies on applying PCR at various stages of the computation. We analyze its performance and show that it increases the survival-probability of various strands to acceptable proportions. Our second approach relies on changing the method by which information is encoded on DNA strands. This encoding is likely to reduce false negative errors during the bead separation procedure. 1 Introduction In the short history of DNA (deoxyribonucleic acid) based computing there have already been a number of exciting results. It all started with Adleman's [A] beautiful insight that showed that biological experiments could solve the Directed Hamiltonian Path problem (DHP). Then, Lipton [L] showed how to use DNA to solve more general problems, namely to find satisfying assignments for arbitrary (direct...

Motivated partly by the resurgence of neural computation research, and partly by advances in device technology, there has been a recent increase of interest in analog, continuous-time computation. However, while special-case algorithms and devices are being developed, relatively little work exists on the general theory of continuous-time models of computation. In this paper, we survey the existing models and results in this area, and point to some of the open research questions. 1 Introduction After a long period of oblivion, interest in analog computation is again on the rise. The immediate cause for this new wave of activity is surely the success of the neural networks "revolution", which has provided hardware designers with several new numerically based, computationally interesting models that are structurally sufficiently simple to be implemented directly in silicon. (For designs and actual implementations of neural models in VLSI, see e.g. [30, 45]). However, the more fundamental...

The maximum number of strands used is an important measure of a molecular algorithm's complexity. This measure is also called the volume used by the algorithm. Every problem that can be solved by an NP Turing machine with b(n) binary nondeterministic choices can be solved by molecular computation in a polynomial number of steps, with four test tubes, in volume 2 b(n) . We identify a large class of recursive algorithms that can be implemented using bounded nondeterminism. This yields improved molecular algorithms for important problems like 3-SAT, independent set, and 3-colorability. 1. A model of molecular computing Molecular computation was first studied in [1, 20]. The models we define were inspired as well by the work of [3, 28]. A molecular sequence is a string over an alphabet \Sigma (we can use any alphabet we like, encoding characters of \Sigma by finite sequences of base pairs). A test tube is a multiset of molecular sequences. We describe the allowable operations below. Whe...

Adleman's [Adl94] successful solution of a seven-vertex instance of the NP-complete Hamiltonian Path problem by recombinant DNA technology initiated the field of biological computing. We propose a very different model of molecular computing based on the biochemistry of RNA editing and RNA translation. In our model, individual molecules become fully capable general purpose computers. 1 Introduction Our goal in this paper is to show how chemically plausible modifications of well-understood biological systems can be used to construct general purpose processors out of individual molecules. To this end, we summarize basic biochemistry in Section 3, in order to make the technological proposals of Sections 4 and 5 understandable. Scientific understanding of the molecular basis for cell biology has grown enormously in recent years. The cell is now understood as a computational system: its program resides in DNA , and its state in the distribution of chemical compounds and electrical charges. ...

The number of molecular strands used by a molecular algorithm is an important measure of the algorithm's complexity. This measure is also called the volume used by the algorithm. We prove that three important polynomial-time models of molecular computation with bounded volume are equivalent to models of polynomial-time Turing machine computation with bounded nondeterminism. Without any assumption, we show that the Split operation does not increase the power of polynomial-time molecular computation. Assuming a plausible separation between Turing machine complexity classes, the Amplify operation does increase the power of polynomial-time molecular computation. 1. Introduction Molecular computation was first studied in [1, 15], which identified the number of molecular strands used as an important resource. This measure is also Research performed at Yale University and at the University of Maryland. Supported in part by the National Science Foundation under grant CCR-8958528, CCR-94154...

Early papers on biological computing focussed on combinatorial and algorithmic issues, and worked with intentionally oversimplified chemical models. In this paper, we reintroduce complexity to the chemical model by considering the effect problem size has on the initial concentrations of reactants, and the effect this has in turn on the rate of production and quantity of final reaction products. We give a sobering preliminary analyses of Adleman's technique for solving Hamiltonian path. Even on the simplest problems, the annealling phase of Adleman's technique requires time\Omega\Gamma n 2 ) rather than the O(log n) complexity given by a computationally inspired but chemically naive analysis. On more difficult problems, not only does the rate of production of witnessing molecules drop exponentially in problem size, the final yield also drops exponentially. These issues are not objections to biological computing per se, but rather difficulties to be overcome in its development as a v...

We survey the theoretical use of DNA computing to solve intractable problems. We also discuss the relationship between problems in DNA computing and questions in complexity theory. 1. Introduction Adleman's pioneering experiment [1] opened the possibility that moderately large instances of NP-complete problems might be solved via techniques from molecular biology. Since then numerous papers have explored more efficient molecular algorithms for particular problems in NP [27, 10, 3, 30, 8, 20, 21, 18], molecular solutions to PSPACE-complete problems [7, 37], and fault tolerant molecular algorithms [12, 25]. Other papers have examined the relationships between molecular complexity classes and classical complexity classes [38, 19]. We will survey some of these advances in this paper. For previous surveys in DNA computing, see [24, 36, 34, 32]. 2. Biological Background DNA is the storage medium for genetic information. It is composed of units called nucleotides, distinguished by the che...

Early papers on biological computing focussed on combinatorial and algorithmic issues, and worked with intentionally oversimplified chemical models. In this paper, we reintroduce complexity to the chemical model by considering the effect problem size has on the initial concentrations of reactants, and the effect this has in turn on the rate of production and quantity of final reaction products. We give a sobering preliminary analyses of Adleman's technique for solving Hamiltonian path. Even on the simplest problems, the annealling phase of Adleman's technique requires time\Omega\Gamma n 2 ) rather than the O(log n) complexity given by a computationally inspired but chemically naive analysis. On more difficult problems, not only does the rate of production of witnessing molecules drop exponentially in problem size, the final yield also drops exponentially. These issues are not objections to biological computing per se, but rather difficulties to be overcome in its development as a v...

In 1994 Adleman published the description of a lab experiment, where he computed an instance of the Hamiltonian path problem with DNA in test tubes. He initiated a flood of further research on computing with molecular means in theoretical computer science. A great number of models was introduced and examined, concerning their computional power (universality as well as time and space complexity), their efficiency and their error resistance. The main results are presented in this survey.