Abstract

: 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...

Citations

759	A course in computational algebraic number theory, volume 138 of Graduate Texts in Mathematics - Cohen - 1993
524	Molecular computation of solutions to combinatorial problem - Adleman - 1994