Cut, paste and filter

• Authors: Peggy Sullivan
• Venue: Discrete Applied Mathematics
• Year: 2003

We study the combined and separate effects of three parts of finite multi-test-tube cut and paste DNA computing. First, we reformulate the ideas of Csuhaj-Varjú et al. (Comput. AI 15(2-3) (1996) 211), Freund (Pacific Symposium on Biocomputing, World Scientific Publishing Co., Singapore, 1997), and Priese et al. (in: L. Hunter, R.B. Altman, A. Kieth Dunker, T. Klein (Eds.), Pacific Symposium on Biocomputing, World Scientific Publishing Co., Singapore, 1998, pp. 547-558) about multi-test-tube splicing DNA computing in terms of cutting and pasting as in Pixton's work (Theoret. Comput. Sci. 234 (2000) 135). As Pixton shows (Discrete Appl. Math. 69 (1996) 101; Theoret. Comput. Sci. 234 (2000) 135) with just finite cutting and pasting only regular sets can be obtained from a finite set of initial molecules. The others cited above show that if filtering is allowed between a finite number of test-tubes in which finite splicing occurs then any recursively enumerable set can be obtained using finite sets of initial test-tube contents (Comput. AI 15(2-3) (1996) 211; in: Developments in Language Theory, Aachen, July 6-9, 1999, pp. 275-286; in: L. Hunter, R.B. Altman, A. Kieth Dunker, T. Klein (Eds.), Pacific Symposium on Biocomputing, World Scientific Publishing Co, Singapore, 1998, pp. 547-558). We confirm this result for cutting and pasting. Second, we show that when only finite pasting and filtering between tubes with finite initial contents are allowed then the result must be context free and that any context free language can be so obtained. Finally, we consider several forms of filtering and several ways of combining filtering with cutting, pasting or splicing and show that all are equivalent.