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Concurrency, Security, and Puzzles pp 185–202Cite as

Discrete Random Variables Over Domains, Revisited

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10160))

Abstract

We revisit the construction of discrete random variables over domains from [15] and show how Hoare’s “normal termination” symbol \(\checkmark \) can be used to achieve a more expressive model. The result is a natural model of flips of a coin that supports discrete and continuous (sub)probability measures. This defines a new random variables monad on BCD, the category of bounded complete domains, that can be used to augment semantic models of demonic nondeterminism with probabilistic choice. It is the second such monad, the first being Barker’s monad for randomized choice [3]. Our construction differs from Barker’s monad, because the latter requires the source of randomness to be shared across multiple users. The monad presented here allows each user to access a source of randomness that is independent of the sources of randomness available to other users. This requirement is useful, e.g., in models of crypto-protocols.

M. Mislove—Work partially supported by AFOSR Grant FA9550-13-1-0135-1.

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Acknowledgement

The author wishes to thank Tyler Barker for some very helpful discussions on the topic of monads of random variables.

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Authors and Affiliations

  1. Department of Computer Science, Tulane University, New Orleans, Louisiana, 70118, USA

    Michael Mislove

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  1. Michael Mislove
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Correspondence to Michael Mislove .

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Editors and Affiliations

  1. University of Oxford, Oxford, United Kingdom

    Thomas Gibson-Robinson

  2. University of Oxford, Oxford, United Kingdom

    Philippa Hopcroft

  3. University of Warwick, Coventry, United Kingdom

    Ranko Lazić

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Mislove, M. (2017). Discrete Random Variables Over Domains, Revisited. In: Gibson-Robinson, T., Hopcroft, P., Lazić, R. (eds) Concurrency, Security, and Puzzles. Lecture Notes in Computer Science(), vol 10160. Springer, Cham. https://doi.org/10.1007/978-3-319-51046-0_10

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  • DOI: https://doi.org/10.1007/978-3-319-51046-0_10

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