How efficiently can room at the bottom be traded away for speed at the top?

• Authors: Pilar De La Torre
• Venue: Natural Computing: an international journal
• Year: 2003

Given exponential 2n space, we know that anAdleman-Lipton computation can decide many hard problems – such asboolean formula and boolean circuit evaluation – in a number ofsteps that is linear in the problem size n. We wish to betterunderstand the process of designing and comparing bio-molecularalgorithms that trade away weakly exponential space to achieve as low arunning time as possible, and to analyze the efficiency of their spaceand time utilization relative to those of their best extantclassical/bio-molecular counterparts. We propose a randomizedframework which augments that of the sticker model of Roweis et al. toprovide an abstract setting for analyzing the space-time efficiency ofboth deterministic and randomized bio-molecular algorithms. We exploreits power by developing and analyzing such algorithms for theCovering Code Creation (CCC) and k-SAT problems. Inthe process, we uncover new classical algorithms for CCC andk-SAT that, while exploiting the same space-time trade-off asthe best previously known classical algorithms, are exponentially moreefficient than them in terms of space-time product utilization. Thiswork indicates that the proposed abstract bio-molecular setting forrandomized algorithm design provides a logical tool of independentinterest.