Abstract
We illustrate a procedure for solving instances of the Boolean satisfiability (SAT) problem by xeroxing onto transparent plastic sheets. Suppose that m clauses are given in which n variables occur and that the longest clause contains k literals. The associated instance of the SAT problem can be solved by using a xerox machine to form only n+2k+m successive transparencies. The applicability of this linear time algorithm is limited, of course, by the increase in the information density on the transparencies when n is large. This same scheme of computation can be carried out by using photographic or other optical processes. This work has been developed as an alternate implementation of procedures previously developed in the context of aqueous (DNA) computing.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Cook SA (1971) The complexity of theorem-proving procedures. In: Proceedings of the 3rd annual ACM symposium on theory of computing. Association for Computing Machinery, New York, pp 151–158
Garey MR, Johnson DS (1979) Computers and intractability—a guide to the theory of NP-completeness. Freeman, San Francisco
Head T (2001) Splicing systems, aqueous computing, and beyond. In: Antoniou I, Calude CS, Dineen MJ (eds) Unconventional models of computation UMC’2K. Springer, Berlin, pp 68–84
Head T (2002) An aqueous algorithm for finding the bijections in a binary relation. In: Brauer W, Ehrig H, Karhumaki J, Salomaa A (eds) Formal and natural computing: essays dedicated to Grzegorz Rozenberg. Lecture notes in computer science, vol 2300. Springer, Berlin, pp 354–360
Head T (2007) Photocomputing: explorations with transparency & opacity. Parallel Process Lett 17:339–347
Head T, Gal S (2006) Aqueous computing: writing on molecules dissolved in water. In: Chen J, Jonoska N, Rozenberg G (eds) Nanotechnology: science and computation. Springer, Berlin, pp 321–331
Head T, Rozenberg G, Bladergroen R, Breek CKD, Lomerese PHM, Spaink H (2000) Computing with DNA by operating on plasmids. Bio Syst 57:87–93
Head T, Chen X, Yamamura M, Gal S (2002) Aqueous computing: a survey with an invitation to participate. J Comput Sci Technol 17:672–681
Henkel C, Bladergroen R, Balog C, Deelder A, Head T, Rozenberg G, Spaink H (2005) Protein output for DNA computing. Nat Comput 4:1–10
Pagano AM, Gal S (2007) An approach for using modified nucleotides in aqueous DNA computing. In: Proceedings of the 13th international computing workshop, Memphis, TN
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Head, T. (2009). Parallel Computing by Xeroxing on Transparencies. In: Condon, A., Harel, D., Kok, J., Salomaa, A., Winfree, E. (eds) Algorithmic Bioprocesses. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88869-7_31
Download citation
DOI: https://doi.org/10.1007/978-3-540-88869-7_31
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-88868-0
Online ISBN: 978-3-540-88869-7
eBook Packages: Computer ScienceComputer Science (R0)