(DNA) computing by carving

Abstract

Inspired by the experiments reported recently in the emerging area of DNA computing, we consider a somewhat unusual type of a computation strategy: generate a (large) set of candidate solutions of a problem, then remove the non-solutions such that what remains is the set of solutions. We call this a computation by carving. This leads both to a speculation with possible important consequences and to interesting theoretical computer science (formal language) questions. The speculation is that in this way we can “compute” non-recursively enumerable languages, because the family of recursively enumerable languages is not closed under complementation. The formal language theory questions concern sequences of languages with certain regularities, needed as languages to be extracted from the total language of candidate solutions of a problem. Specifically, we consider sequences of languages obtained by starting from a given regular language and iteratively applying to it a given finite state sequential transducer (a gsm). Computing by carving with respect to such a sequence of languages can identify all context-sensitive languages and can also lead to non-recursively enumerable languages (but not all recursively enumerable languages can be obtained in this way). In practical circumstances, the carving process should be finite, hence, in general, approximations of the desired language are obtained. We also briefly discuss this aspect.