Bacteria employ restriction enzymes to cut or restrict DNA at or near specific words in a unique way. Many restriction enzymes cut the two strands of double-stranded DNA at different positions leaving overhangs of single-stranded DNA. Two pieces of DNA may be rejoined or ligated if their terminal overhangs are complementary. Using these operations fragments of DNA, or oligonucleotides, may be inserted and deleted from a circular piece of plasmid DNA. We propose an encoding for the transition table of a Turing machine in DNA oligonucleotides and a corresponding series of restrictions and ligations of those oligonucleotides that, when performed on circular DNA encoding an instantaneous description of a Turing machine, simulate the operation of the Turing machine encoded in those oligonucleotides. DNA based Turing machines have been proposed by Charles Bennett but they invoke imaginary enzymes to perform the state-symbol transitions. Our approach differs in that every operation can be pe...

In [Winfree] it was shown that the DNA primitives of Separate, Merge, and Amplify were not sufficiently powerful to invert functions defined by circuits in linear time. Dan Boneh et al [Boneh] show that the addition of a ligation primitive, Append, provides the missing power. The question becomes, "How powerful is ligation? Are Separate, Merge, and Amplify necessary at all?" This paper proposes to informally explore the power of annealing and ligation for DNA computation. We conclude, in fact, that annealing and ligation alone are theoretically capable of universal computation. 1 Introduction When Len Adleman introduced the paradigm of using DNA to solve combinatorial problems [Adleman], his computational scheme involved two distinct phases. To solve the directed Hamiltonian path problem, he first mixed together in a test tube a carefully designed set of DNA oligonucleotide "building blocks", which anneal to each other and are ligated to create long strands of DNA representing paths t...

Winfree (1996) proposed a Turing-universal model of DNA self-assembly. In this abstract model, DNA double-crossover molecules self-assemble to form an algorithmically-patterned two-dimensional lattice. Here, we develop a more realistic model based on the thermodynamics and kinetics of oligonucleotide hydridization. Using a computer simulation, we investigate what physical factors influence the error rates, i.e., when the more realistic model deviates from the ideal of the abstract model. We find, in agreement with rules of thumb for crystal growth, that the lowest error rates occur at the melting temperature when crystal growth is slowest, and that error rates can be made arbitrarily low by decreasing concentration and increasing binding strengths. 1 Introduction Early work in DNA computing (Adleman 1994; Lipton 1995; Boneh et al. 1996; Ouyang et al. 1997) showed how computations can be accomplished by first creating a combinatorial library of DNA and then, through successiv...

We demonstrate that DNA computers can simulate Boolean circuits with a small overhead. Boolean circuits embody the notion of massively parallel signal processing and are frequently encountered in many parallel algorithms. Many important problems such as sorting, integer arithmetic, and matrix multiplication are known to be computable by small size Boolean circuits much faster than by ordinary sequential digital computers. This paper shows that DNA chemistry allows one to simulate large semi-unbounded fan-in Boolean circuits with a logarithmic slowdown in computation time. Also, for the class NC 1 , the slowdown can be reduced to a constant. In this algorithm we have encoded the inputs, the Boolean AND gates, and the OR gates to DNA oligonucleotide sequences. We operate on the gates and the inputs by standard molecular techniques of sequence-specific annealing, ligation, separation by size, amplification, sequence-specific cleavage, and detection by size. Additional steps of amplifica...

Recently Adleman [1] has shown that a small traveling salesman problem can be solved by molecular operations. In this paper we show how the same principles can be applied to breaking the Data Encryption Standard (DES). Our method is based on an encoding technique presented in Lipton [8]. We describe in detail a library of operations which are useful when working with a molecular computer. We estimate that given one arbitrary (plain-text, cipher-text) pair, one can recover the DES key in about 4 months of work. Furthermore, if one is given cipher-text, but the plain text is only known to be one of several candidates then it is still possible to recover the key in about 4 months of work. Finally, under chosen cipher-text attack it is possible to recover the DES key in one day using some preprocessing. 1 Introduction Due to advances in molecular biology it is nowadays possible to create a soup of roughly 10 18 DNA strands that fits in a small glass of water. Adleman [1] has shown that e...

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...

In this paper we show that DNA computers are especially useful for running algorithms which are based on dynamic programming. This class of algorithms takes advantage of the large memory capacity of a DNA computer. We present algorithms for solving certain instances of the knapsack problem using a dynamic programming approach. Unlike other algorithms[1, 12] for DNA computers, which are brute force, dynamic programming is the same algorithm one would use to solve (smaller) problems on a conventional computer. 1 Introduction In a recent seminal paper [1], Adleman introduced the idea of computing using DNA molecules. Adleman's techniques were then generalized by Lipton [12] who showed that formula-SAT can be solved on a DNA computer. These algorithms essentially use a brute force approach to solve hard combinatorial problems. This approach is interesting due to the massive parallelism available in DNA computers. However, the brute force approach is limited by the number of DNA molecules ...

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.

DNA computing has recently generated much interest as a result of pioneering work by Adleman and Lipton. Their DNA algorithms worked on graph representations but no indication was provided as to how information on the arcs between nodes on a graph could be handled. The aim of this paper is to extend the basic DNA algorithmic techniques of Adleman and Lipton by proposing a method for representing simple arc information --- in this case, distances between cities in a simple map. It is also proposed that the real potential of DNA computing for solving computationally hard problems will only be realised when algorithmic steps which currently require manual intervention are replaced by executable DNA which operate on DNA strands in test-tubes. 1 Computationally hard problems and DNA computing Both Adleman's (1994) and Lipton's (1995) algorithms deal with graphs where there are no labels on the arcs, nor is there any indication provided as to how such labels can be handl...