"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  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 .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.
Proceedings of the 10th WSEAS international conference on Computers; 07/2006
"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) "
[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.
[Show abstract][Hide abstract] ABSTRACT: In this paper we propose an approach which increases productivity of DNA com-putations by performing laboratory operations in parallel. We consider algorithms implemented in Parallel Filtering Model proposed by M. Amos, A. Gibbons and D. Hodgson. Basic operation of this model can be implemented using parallel labora-tory operations. We show that by using this approach time complexity of some algo-rithms may be increased from polynomial to logarithmic. We also examine amount of DNA strands used and number of laboratory equipment ("tubes") needed for proposed implementation.
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