Biomedical subjects

Dafa Li

Publications and source records attributed to Dafa Li.

3 recordsLinked to original sources

PubMed2006

Scalability of the surface-based DNA algorithm for 3-SAT.

Since Adleman first proposed DNA computing for the Hamiltonian path problem, several authors have reported DNA computing for 3-SAT. Previous research presented DNA computing on surfaces and demonstrated how to solve a four-variable four-clause instance of 3-SAT, and claimed that the surface-based approach was designed to scale up to larger problems. In this paper we establish an error model for the incomplete "mark" and imperfect "destroy" operations. By using the error model we argue that no matter how large the "mark" and "destroy" rates are we can always give satisfiable instances of 3-SAT such that no DNA strands remain on the surface at the end of the computation. By the surface-based approach the satisfiable instances of 3-SAT would be misdetermined to be unsatisfiable. Thus, the error leads to an incorrect result of the SAT computation. Furthermore, given the "mark" rate p and the "not-destroy" rate rho, we find that the approach can only solve at most N-variable instances of 3-SAT problems, where N=[(2+beta(2)+2+2 square root beta (2))/beta(2)] in which beta=1-1/(p+rhoq) and q=1-p and [a] is the greatest integer less than a or equal to a.

Algorithms↗

PubMed2005

The surface-based approach for DNA computation is unreliable for SAT.

Previous research presented DNA computing on surfaces, which applied to each clause three operations:"mark","destroy", and "unmark", and demonstrated how to solve a four-variable four-clause instance of the 3-SAT. It was claimed that only the strands satisfying the problem remained on the surface at the end of the computation and the surface-based approach was capable of scaling up to larger 3-SAT problems. Accordingly, the identities of the strands were only determined in the"readout" step for the correct solutions to the problem without checking if the strands really satisfied the problem. Thus, based on the claim above, the surface-based approach became a polynomial-time algorithm. In this paper, we show that for some instance of SAT, at the end of the computation all the remaining strands falsify the instance. However, by the previous claim all the strands falsifying the problems would be regarded as the correct solutions to the problems. Therefore, the DNA computing on surfaces is unreliable. For this reason, it is necessary to add a "verify" step after the "readout" step to check if the strands remaining on the surface at the end of the computation really satisfy the problem.

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PubMed2003

Hairpin formation in DNA computation presents limits for large NP-complete problems.

Recently, several DNA computing paradigms for NP-complete problems were presented, especially for the 3-SAT problem. Can the present paradigms solve more than just trivial instances of NP-complete problems? In this paper we show that with high probability potentially deleterious features such as severe hairpin loops would be likely to arise. If DNA strand x of length n and the 'complement' of the reverse of x have l match bases, then x forms a hairpin loop and is called a (n,l)-hairpin format. Let gamma=2l/n. Then gamma can be considered as a measurement of the stability of hairpin loops. Let p(n,l) be the probability that a n-mer DNA strand is a (n,l)-hairpin format, and q(n,l)((m)) be the probability that m ones are chosen at random from 4(n) n-mer oligonucleotides such that at least one of the m ones is a (n,l)-hairpin format. Then, q(n,l)((m))=1-(1-p(n,l))(m)=mp(n,l). If we require q(n,l)((m))<a, where a<1, then m<ln(1-a)/ln(1-p(n,l))=a/p(n,l). It means that we can only solve the instances of size m of NP-complete problems. Clearly the greater p(n,l), the smaller m, and the smaller a the smaller m. In this paper, we show p(n,l) is high. Therefore, the present DNA computing paradigms cannot solve large NP-complete problems. For example, if n=20, used in Adleman and Lipton's paradigm, gamma=50% and a=50%, then m is almost 12.

Algorithms↗