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Unifying Probability

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Unifying Theories of Programming (UTP 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4010))

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Abstract

We demonstrate a new unification of probability with standard computation in which a nonzero chance of disaster is treated as disaster. Laws and a Galois connection with the more traditional probabilistic model are provided. Reversibility in the probabilistic guarded-command language is discussed. Finally the formalism is applied to unify quantum computation and cryptography within the probabilistic method.

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References

  1. Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proc. IEEE Conference on Computers, Systems and Signal processing, Bangalore, pp. 175–179 (1984)

    Google Scholar 

  2. Bennett, C.H., Brassard, G., Robert, J.-M.: Privacy amplification by public discussion. SIAM Journal of Computing 17(2), 210–229 (1988)

    Article  MathSciNet  Google Scholar 

  3. Bennett, C.H.: Quantum cryptography using any two nonorthogonal states. Physical Review Letters 68(21), 3121–3124 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  4. Butler, M.J., Hartel, P.: Reasoning about Grover’s quantum search algorithm using probabilistic wp. ACM Transactions on Programming Languages and Systems 21(3), 417–430 (1999)

    Article  Google Scholar 

  5. Grover, L.: A fast quantum mechanical algorithm for database search. In: Proceedings of 28th ACM STOC, pp. 212–219 (1996)

    Google Scholar 

  6. Gruska, J.: Quantum Computing. Advanced Topics in Computer Science. McGraw-Hill International, UK (1999)

    Google Scholar 

  7. Harel, D.: Algorithmics: The Spirit of Computing, 2nd edn. Addison Wesley, Reading (1992)

    MATH  Google Scholar 

  8. He, J., Seidel, K., McIver, A.K.: Probabilistic models for the guarded command language. Science of Computer Programming 28, 171–192 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hehner, E.R.: Probabilistic predicative programming. In: Kozen, D. (ed.) MPC 2004. LNCS, vol. 3125, pp. 169–185. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  10. Hoare, C.A.R., He, J.: Unifying Theories of Programming. Prentice Hall, Englewood Cliffs (1998)

    Google Scholar 

  11. Landauer, R.: Irreversibility and heat generated in the computing process. IBM Journal of Research and Development 5 (1961)

    Google Scholar 

  12. McIver, A.K., Morgan, C.C.: Abstraction, Refinement and Proof for Probabilistic Systems. Springer Monographs in Computer Science (2005)

    Google Scholar 

  13. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  14. Sanders, J.W., Zuliani, P.: Quantum Programming. In: Backhouse, R., Oliveira, J.N. (eds.) MPC 2000. LNCS, vol. 1837, pp. 80–99. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  15. Stoddart, W.J., Zeyda, F., Lynas, R.: A design-based model of reversible computation. In: Dunne, S., Stoddart, B. (eds.) UTP 2006. LNCS, vol. 4010, pp. 63–83. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  16. Wootters, W.K., Zurek, W.H.: A single quantum cannot be cloned. Nature 299(5886), 802–803 (1982)

    Article  Google Scholar 

  17. Zuliani, P.: Logical reversibility. IBM Journal of Research and Development 45(6), 807–818 (2001)

    Article  Google Scholar 

  18. Zuliani, P.: Compiling Quantum Programs. Acta Informatica 41(7-8), 435–474 (2005)

    Article  MathSciNet  MATH  Google Scholar 

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© 2006 Springer-Verlag Berlin Heidelberg

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He, J., Sanders, J.W. (2006). Unifying Probability. In: Dunne, S., Stoddart, B. (eds) Unifying Theories of Programming. UTP 2006. Lecture Notes in Computer Science, vol 4010. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11768173_11

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  • DOI: https://doi.org/10.1007/11768173_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34750-7

  • Online ISBN: 978-3-540-34752-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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