Is optimal solution of every NP-complete or NP-hard problem determined from its characteristic for DNA-based computing.
Cook's Theorem [Cormen, T.H., Leiserson, C.E., Rivest, R.L., 2001. Introduction to Algorithms, second ed., The MIT Press; Garey, M.R., Johnson, D.S., 1979. Computer and Intractability, Freeman, San Fransico, CA] is that if one algorithm for an NP-complete or an NP-hard problem will be developed, then other problems will be solved by means of reduction to that problem. Cook's Theorem has been demonstrated to be correct in a general digital electronic computer. In this paper, we first propose a DNA algorithm for solving the vertex-cover problem. Then, we demonstrate that if the size of a reduced NP-complete or NP-hard problem is equal to or less than that of the vertex-cover problem, then the proposed algorithm can be directly used for solving the reduced NP-complete or NP-hard problem and Cook's Theorem is correct on DNA-based computing. Otherwise, a new DNA algorithm for optimal solution of a reduced NP-complete problem or a reduced NP-hard problem should be developed from the characteristic of NP-complete problems or NP-hard problems.
Guo
Minyi
M
Department of Computer Software, The University of Aizu, Aizu-Wakamatsu City, Fukushima 965-8580, Japan. minyi@u-aizu.ac.jp
Chang
Weng-Long
WL
Ho
Machael
M
Lu
Jian
J
Cao
Jiannong
J
D000465:Algorithms; D019295:Computational Biology / Q000379:methods; D003198:Computer Simulation; D039301:Computers, Molecular; D003205:Computing Methodologies; D004247:DNA / Q000737:chemistry* / Q000378:metabolism*; D008954:Models, Biological; D008956:Models, Chemical; D009716:Numerical Analysis, Computer-Assisted
D004247:DNA