Whiplash PCR for O(1) Computing

This paper reviews the experimental technique of whiplash PCR, as introduced in Hagiya et al. (in press), and proposes a model of computation based on this technique in combination with assembly PCR (Stemmer et al. 1995). In this model, based on GOTO graphs, a number of NP-complete problems can be solved in O(1) biosteps, including branching program satisfiability, the independent set problem, and the Hamiltonian path problem. In addition, we propose a simple extension of the experimental technique that allows single DNA strands to simulate the execution of a feed-forward circuit, giving rise to a solution to the circuit satisfiability problem in O(1) biosteps.