Adleman demonstrate that we can deoxyribonucleic acid (DNA) strands to solve an instance of the Hamiltonian path problem (HPP). One year later, Lipton solved another NP hard problem. In this paper, we use this model for developing a new DNA algorithm to solve longest and shortest path with forbidden pairs. Our algorithm works in polynomial time.

In this paper, we consider a procedure for solving the shortest path problem in the Adleman–Lipton model. The procedure works in O(n) steps for the shortest path problem of an edge-weighted graph with n vertices. 2006 Elsevier Inc. All rights reserved.

It is shown first by Adleman that deoxyribonucleic acid (DNA) strands could be employed towards calculating solution to an instance of the NP-complete Hamiltonian Path Problem (HPP). Lipton also demonstrated that Adleman’s techniques could be used to solve the satisfiability (SAT) problem. In this paper, it is demonstrated how the DNA operations presented by Adleman and Lipton can be used to de...

We show that the class Sp2 is contained in ZPP NP. The proof uses universal hashing, approximate counting and witness sampling. As a consequence, a collapse first noticed by Samik Sengupta that the assumption NP has small circuits collapses PH to Sp2 becomes the strongest version to date of the Karp–Lipton Theorem. We also discuss the problem of finding irrefutable proofs for Sp2 in ZPPNP. © 20...

www.thelancet.com/neurology Published online March 26, 2015 http://dx.doi.org/10.1016/S1474-4422(15)00011-3 1 Stuart Lipton was up in the middle of the night fielding emails when he saw his first UFO. No ordinary flying saucer, this UFO was staring up from the text of the review article he was struggling to finalise. The sticking point was to come up with finding a catchy way to explain the uni...

This work was partially funded by the French Space Agency (CNES) and Cognitech Inc. We would like to specially thank JeanMichel Morel for his encouragement, support, ideas, and for introducing us to Gestalt-based image analysis. A. Almansa would also like to thank Lenny Rudin and Pascal Monasse for useful discussions, references, and motivation to address this problem, as well as for adapting a...

Recent work demonstrates that learning to understand noise-vocoded (NV) speech alters sublexical perceptual processes but is enhanced by the simultaneous provision of higher-level, phonological, but not lexical content (Hervais-Adelman, Davis, Johnsrude, & Carlyon, 2008), consistent with top-down learning (Davis, Johnsrude, Hervais-Adelman, Taylor, & McGettigan, 2005; Hervais-Adelman et al., 20...