# Unwinding performance and power on Colossus, an unconventional computer

- 243 Downloads
- 1 Citations

## Abstract

In 1944 the computing machine known as Colossus became operational in support of British cryptanalysis and decryption of German High Command wireless traffic. This first electronic digital and very unconventional computer was not a stored-program general purpose computer in today’s terms, despite printed claims to the contrary. At least one of these asserts Colossus was a Turing machine. While an appropriate Turing machine can simulate the operation of Colossus, that is not an argument for generality of computation. Nor does the behavior of Colossus resemble that of a Turing machine, much less a universal Turing machine (UTM). Nonetheless, we shall see that a UTM could have been implemented on a clustering of the ten Colossus machines installed at Bletchley Park, England, by the end of WWII in 1945. Improvements require even fewer machines. Several advances in input, output, speed, processing, and applications—within the hardware capability of the time and respectful of the specification of Colossus—are also offered.

## Keywords

Colossus Universal computation Small UTM Preclassical computers## Notes

### Acknowledgments

I am deeply grateful to the University of San Francisco Faculty Development Fund, for sponsoring participation in UC09 and for providing stipends to the graduate research assistants who developed the Colossus simulator and worked briefly on the UTM project; the UC09 organizers and reviewers, for cheerful and brilliant hospitality and acceptance of Wells (2009); Mike Stannett, for inclusion in Hypernet and the invitation to speak in the Hypercomputation Workshop at UC09; Jack Copeland, for starting me on the path to hypercomputation in 2000 and to Colossus soon after, and encouraging my participation in UC09; Brian Randell, for lengthy and valuable email exchanges; Wen Dong, for excellence as a student and collaborator; Vaughan Pratt, for the gift of the Hewitt machine and other useful discussions on small UTMs; Damien Woods, for enthusiastic conversation at UC09; the referees, for their kind grace; José Félix Costa, for opening the way and making it easy; and the One True Being, for being.

## References

- Andresen SL (2001) Donald Michie: secrets of Colossus revealed. IEEE Intell Syst 16(6):82–83Google Scholar
- Beckman B (2000) Codebreakers: Arne Beurling and the Swedish crypto program during World War II. American Mathematical Society, ProvidenceGoogle Scholar
- Chandler WW (1983) The installation and maintenance of Colossus. IEEE Ann Hist Comput 5:260–262CrossRefGoogle Scholar
- Cleland CE (1995) Effective procedures and computable functions. Minds Mach 5:9–23CrossRefGoogle Scholar
- Cleland CE (2001) Recipes, algorithms, and programs. Minds Mach 11:219–237zbMATHCrossRefGoogle Scholar
- Cleland CE (2004) The concept of computability. Theor Comput Sci 317:209–225MathSciNetzbMATHCrossRefGoogle Scholar
- Cleland CE (2007) The Church-Turing thesis: a last vestige of a failed mathematical program. In: Olszewksi A, Woleński J, Janusz R (eds) Church’s thesis after seventy years. Ontos Verlag, Berlin, pp 119–146Google Scholar
- Coombs AWM (1983) The making of Colossus. IEEE Ann Hist Comput 5:253–259CrossRefGoogle Scholar
- Copeland BJ (2004) Colossus: its origins and originators. IEEE Ann Hist Comp 26:38–45MathSciNetCrossRefGoogle Scholar
- Copeland BJ (ed) (2005) Alan Turing’s Automatic Computing Engine: the master codebreaker’s struggle to build the modern computer. Oxford University Press, OxfordzbMATHGoogle Scholar
- Copeland BJ (ed) (2006) Colossus: the secrets of Bletchley Park’s codebreaking computers. Oxford University Press, OxfordGoogle Scholar
- Copeland BJ (2007) Tunny and Colossus: breaking Lorenz Schlüsellzusatz traffic. In: de Leeuw K, Bergstra JA (eds) The history of information security: a comprehensive handbook. Elsevier Science, Amsterdam, pp 447–478. A revised, illustrated version of this article has appeared online: Copeland BJ (2010) Colossus: breaking the German Tunny code at Bletchley Park—an illustrated history. In: The Rutherford Journal (2010). http://www.rutherfordjournal.org/article030109.html. Accessed 25 July 2010
- Cragon HG (2003) From Fish to Colossus. Cragon Books, DallasGoogle Scholar
- Dong W, Chen W, Long K (2003) USF Colossus simulator. http://www.cs.usfca.edu/~wdong/. Accessed 25 July 2010
- Fant K, Brandt S (1996) Null Convention Logic, a complete and consistent logic for asynchronous digital circuit synthesis. In: Proceedings of the international conference on application specific systems, architectures, and processors (ASAP 96). IEEE Computer Society Press, Los Alamitos, pp 261–273Google Scholar
- Flowers TH (1983) The design of Colossus. IEEE Ann Hist Comput 5:239–252CrossRefGoogle Scholar
- Foundations of Mathematics Archive (2007). http://www.cs.nyu.edu/pipermail/fom/2007-October/thread.html. Accessed 25 July 2010
- Fox B, Webb J (1997) Colossal adventures. New Sci 154(2081):38–43Google Scholar
- Gandy R (1988) The confluence of ideas in 1936. In: Herken R (ed) The universal Turing machine: a half-century survey, 1st edn. Oxford University Press, Oxford, pp 51–102Google Scholar
- Gannon P (2006) Colossus: Bletchley Park’s greatest secret. Atlantic Books, LondonGoogle Scholar
- Good IJ (1979) Early work on computers at Bletchley. IEEE Ann Hist Comput 1:38–48MathSciNetCrossRefGoogle Scholar
- Good IJ (1980) Pioneering work on computers at Bletchley. In: Metropolis N, Howlett J, Rota G-C (eds) A history of computing in the twentieth century. Academic Press, New York, pp 31–46Google Scholar
- Good IJ, Michie D, Timms G (1945) General report on Tunny. National Archives Public Records Office, London, HW 25/4 and HW 25/5Google Scholar
- Harcke LJ (2004) Number cards and the Analytical Engine, 19 pp (unpublished)Google Scholar
- Herken R (ed) (1995) The universal Turing machine: a half-century survey, 2nd edn. Springer, BerlinzbMATHGoogle Scholar
- Hewitt A (2007) Universal computation with only 6 rules. http://forum.wolframscience.com/showthread.php?threadid=1432. Accessed 25 July 2010
- Ifrah G (2001) A universal history of computing: from the abacus to the quantum computer (translation from French). Wiley, New YorkGoogle Scholar
- Institute of Druid Technology (2010) Biosphere III. http://www.druidtech.org/biosphere.html. Accessed 25 July 2010
- Kubesh B, Lathem G, Jaggi M, Sinha A, Hall M (2007) Processing system using bitmap array to compress deterministic finite automaton state table allowing direct indexing. US Patent 7,305,383Google Scholar
- Lewis H, Papadimitriou ChH (1997) Elements of the theory of computation, 2nd edn. Prentice Hall, Upper Saddle RiverGoogle Scholar
- Randell B (1976) The Colossus. Technical Report No. 90 (1976), Computing Laboratory, University of Newcastle upon Tyne. Paper presented at the International Research Conference on the History of Computing. Los Alamos Scientific Laboratory, University of California, 10–15 June 1976. Republished as Randell B (1980) The Colossus. In: Metropolis N, Howlett J, Rota G-C (eds) A history of computing in the twentieth century. Academic Press, New York, pp 47–92Google Scholar
- Reilly ED (2003) Milestones in computer science and information technology. Greenwood Press, Westport, p 164Google Scholar
- Rojas R (1998) How to make Zuse’s Z3 a universal computer. IEEE Ann Hist Comput 20:51–54CrossRefGoogle Scholar
- Sale T (2010a) Welcome to Anoraks Corner, speeding up Colossus. http://www.codesandciphers.org.uk/anoraks/lorenz/speedup.htm. Accessed 25 July 2010
- Sale T (2010b) http://www.codesandciphers.org.uk. Accessed 25 July 2010
- Sale T (2010c) http://www.codesandciphers.org.uk/virtualbp/fish/colossus.htm. Accessed 25 July 2010
- Singh S (1999) The code book. Anchor Books, New YorkGoogle Scholar
- Small AW (1944) The special Fish report. Held in the American National Archive and Records Administration (NARA) College Campus, Washington DC. OCR available at http://www.codesandciphers.org.uk/documents/small/smallix.HTM. Accessed 25 July 2010
- Smith A (2008) Universality of Wolfram’s 2,3 Turing machine. http://www.wolframscience.com/prizes/tm23/TM23Proof.pdf. Accessed 25 July 2010
- Tutte WT (1998) FISH and I. Department of Combinatorics and Optimization Monograph 98-39, University of Waterloo, OntarioGoogle Scholar
- Watanabe S (1961) 5-Symbol 8-state and 5-symbol 6-state universal Turing machines. J ACM 8:476–483zbMATHCrossRefGoogle Scholar
- Watanabe S (1972) 4-Symbol 5-state universal Turing machines. J Inf Process Soc Jpn 13:588–592Google Scholar
- Wells B (1982) Pseudorecursive varieties and their implications for word problems. Dissertation, University of California, BerkeleyGoogle Scholar
- Wells B (1996) Pseudorecursive varieties of semigroups—I. Int J Algebra Comput 6:457–510zbMATHCrossRefGoogle Scholar
- Wells B (2004a) A universal Turing machine can run on a cluster of Colossi. Abstr Am Math Soc 25:441Google Scholar
- Wells B (2004b) The architecture of Colossus—the first PC. EE380 Computer Systems Colloquium talk, 4 Feb 2004. Streaming video available at http://www.stanford.edu/class/ee380/, choose Past Colloquia, 2003–2004, click on camera icon. Accessed 25 July 2010
- Wells B (2006) The PC-user’s guide to Colossus. In: Copeland BJ (ed) Colossus: the secrets of Bletchley Park’s codebreaking computers. Oxford University Press, Oxford, pp 116–140Google Scholar
- Wells B (2009) Advances in I/O, speedup, and universality on Colossus, an unconventional computer. In: Calude CS, Costa JF, Dershowitz N, Freire E, Rozenberg G (eds) Unconventional computation. Unconventional Computation, Ponta Delgada, Sept 2009. Lecture Notes in Computer Science, vol 5175. Springer, Berlin, pp 247–261Google Scholar
- Wolfram S (2002) A new kind of science. Wolfram Media, ChampaignzbMATHGoogle Scholar
- Woods D, Neary T (2009) The complexity of small universal Turing machines: a survey. Theor Comput Sci 410:443–450MathSciNetzbMATHCrossRefGoogle Scholar