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19 Citations# The Complexity and Viability of DNA Computations.

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- "Recall that NC 1 defines the class of problems of size n solved by bounded fan-in circuits of O (log n) depth and polynomial size. Amos and Dunne [11] showed that, in spite of ogihara's claim, the time complexity of their proposed algorithm is proportional to the size of the circuit. They propose an algorithm with time proportional to the depth of circuit but their circuit is a NAND-based circuit [3].In addition they claim that they don't use error-prone techniques such as PCR (Polymerase Chain Reaction), but they haven't considered the state that an output of a gate may be the input of two or more gates in the next level, which needs amplification. "

[Show abstract] [Hide abstract]**ABSTRACT:**DNA computing has recently gained intensive attention as an emerging field bridging the gap between computer science and biomolecular science. DNA based computing can be competitively used to simulate various computing models including Boolean circuits because of its potential to offer massive parallelism. In this paper we present a new DNA-based evaluation algorithm for a bounded fan-in circuit consisting of AND and OR gates. The proposed model employs standard bio-molecular techniques. The main advantage of our method is that each level of circuit is capable of containing both AND and OR gates. It is shown that large bounded fan-in circuits can be simulated by the proposed approach with a logarithmic slowdown in computation time.- "If we assume that n = 2 k , this gives the total size (in terms of number of gates) as 2:5(log n)(log n − 1) + 10n − 10 and depth (in gates) as (log n)(log n + 1). Within the context of the strong model from [7] (the main feature of which being the restriction that pour operations are performed in a linear fashion rather than in parallel) an n-input Batcher network can therefore be simulated using K(2:5(log n)(log n − 1) + 10n − 10) volume in 7(log n)(log n + 1) time, where K is a constant representing the number of copies of a single strand required to give reasonable guarantees of correct operation. The coeecient of 7 in the time ÿgure represents the number of separate stages in a single level simulation. "

[Show abstract] [Hide abstract]**ABSTRACT:**DNA computing, or, more generally, molecular computing, is an exciting fast developing interdisciplinary area. Research in this area concerns theory, experiments, and applications of DNA computing. In this paper, we demonstrate the theoretical developments by discussing a number of selected topics. We also give an introduction to the basic structure of DNA and the basic DNA processing tools.- "The properties of this buffer can be separately adjusted to provide optimal discrimination between specific and non-specific binding. This and repeated selections may resolve some of the generic difficulties with specific strand extraction via hybridization (Amos et al., 1997). 2. Avoiding extensive dilution of the transferred DNA. "

[Show abstract] [Hide abstract]**ABSTRACT:**The programmability and the integration of biochemical processing protocols are addressed for DNA computing using photochemical and microsystem techniques. A magnetically switchable selective transfer module (STM) is presented which implements the basic sequence-specific DNA filtering operation under constant flow. Secondly, a single steady flow system of STMs is presented which solves an arbitrary instance of the maximal clique problem of given maximum size N. Values of N up to about 100 should be achievable with current lithographic techniques. The specific problem is encoded in an initial labeling pattern of each module with one of 2N DNA oligonucleotides, identical for all instances of maximal clique. Thirdly, a method for optically programming the DNA labeling process via photochemical lithography is proposed, allowing different problem instances to be specified. No hydrodynamic switching of flows is required during operation -- the STMs are synchronously clocked by an external magnet. An experimental implementation of this architecture is under construction and will be reported elsewhere.

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