@INPROCEEDINGS{Lipton94speedingup, author = {Richard J. Lipton}, title = {Speeding Up Computations via Molecular Biology}, booktitle = {}, year = {1994}, pages = {67--74} }

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: We show how to extend the recent result of Adleman [1] to use biological experiments to directly solve any NP problem. We, then, show how to use this method to speedup a large class of important problems. 1. Introduction In a recent breakthrough Adleman [1] showed how to use biological experiments to solve instances of the famous Hamiltonian Path Problem (HPP). Since this problem is known to be NP-complete it follows that biology can be used to solve any problem from NP. Recall that all problems in NP can be reduced to any NP-complete one. However, this does not mean that all instances of NP problems can be solved in a feasible sense. Adleman solves the HPP in a totally brute force way: he designs a biological system that "tries" all possible tours of the given cities. The speed of any computer, biological or not, is determined by two factors: (i) how many parallel processes it has; (ii) how many steps each can perform per unit time. The exciting point about biology is that the firs...

...ctly search problems. Consider the problem of factoring integers. The inner loop of many fast methods is the search to find y = x 2 mod N so that y factors completely over a given "factor basis&q=-=uot; (see [2]-=- for details). It is clear that we can speedup the naiive search for such any y by a factor of 2 n . The question however is can we use our methods to speedup the current more sophisticated methods? A...

... to use biological experiments to directly solve any NP problem. We, then, show how to use this method to speedup a large class of important problems. 1. Introduction In a recent breakthrough Adleman =-=[1]-=- showed how to use biological experiments to solve instances of the famous Hamiltonian Path Problem (HPP). Since this problem is known to be NP-complete it follows that biology can be used to solve an...