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Abstract Hidden Markov Models: A Monadic Account of Quantitative Information Flow

Annabelle McIver, Carroll Morgan, Tahiry Rabehaja
2015 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science  
However to encode the monadic type with hiding over state X we use DX !D 2 X rather than the conventional X !DX . We illustrate this construction with a very small Haskell prototype.  ...  Index Terms-Abstract Hidden Markov Models, Giry Monad, Quantitative Information Flow. P for each x: X . ⇤ Now for some ⇡: _ X and channel C: X _Y define joint distribution J: X _Y by J=⇡BC.  ...  ACKNOWLEDGEMENTS We're grateful for advice from Franck van Breugel, James Worrell, Tom Schrijvers and other members of IFIP WG 2.1, and for inspiration and insight from the INRIA Princess team.  ... 
doi:10.1109/lics.2015.61 dblp:conf/lics/McIverMR15 fatcat:4mii2ijocjfsdhkkeylvyqnzti

Abstract Hidden Markov Models: a monadic account of quantitative information flow [article]

Annabelle McIver and Carroll Morgan and Tahiry Rabehaja
2018 arXiv   pre-print
We use HMM's as denotations of probabilistic hidden-state sequential programs: for that, we recast them as 'abstract' HMM's, computations in the Giry monad D, and we equip them with a partial order of  ...  However to encode the monadic type with hiding over some state X we use DX→D^2X rather than the conventional X→DX that suffices for Markov models whose state is not hidden.  ...  Acknowledgements We're grateful for advice from Franck van Breugel, James Worrell, Tom Schrijvers and other members of IFIP WG 2.1, and for inspiration and insight from the INRIA Princess team.  ... 
arXiv:1708.01688v2 fatcat:jyy7efnu5vb63h5lhejngrvpnu

Quantitative Security Analysis (Dagstuhl Seminar 12481)

Boris Köpf, Paquale Malacaria, Catuscia Palamidessi, Marc Herbstritt
2013 Dagstuhl Reports  
Corresponding quantitative security analyses bear the potential of becoming an important tool for the rigorous development of practical systems, and a formal foundation for the management of security risks  ...  The high amount of trust put into today's software systems calls for a rigorous analysis of their security.  ...  Markov Processes (for probability without nondeterminism or hiding), Markov Decision Processes (add nondeterminism) and Partially Observable MDP's (add hiding) are mathematical models.  ... 
doi:10.4230/dagrep.2.11.135 dblp:journals/dagstuhl-reports/KopfMP12 fatcat:zlrdsjynqnfv3ehvlybivdnwre

Compositional security and collateral leakage [article]

N. Bordenabe, A. McIver, C Morgan, T. Rabehaja
2016 arXiv   pre-print
In quantitative information flow we say that program Q is "at least as secure as" P just when the amount of secret information flowing from Q is never more than flows from P, with of course a suitable  ...  This secure-refinement order is compositional just when PQ implies C(P) C(Q) for any context C, again with a suitable definition of "context".  ...  A Kantorovich-monadic powerdomain for information hiding, with probability and nondeterminism. In Proc. LiCS 2012, 2012. 21 Annabelle McIver, Larissa Meinicke, and Carroll Morgan.  ... 
arXiv:1604.04983v1 fatcat:rv7hoo32cfaldeucjldu7wrwye

Complete Quasi-Metrics for Hyperspaces, Continuous Valuations, and Previsions [article]

Jean Goubault-Larrecq
2021 arXiv   pre-print
We do this not only for probability distributions, represented as normalized continuous valuations, but also for subprobability distributions, for various hyperspaces, and in general for different brands  ...  The Kantorovich-Rubinshtein metric is an L^1-like metric on spaces of probability distributions that enjoys several serendipitous properties.  ...  Here m X maps ((x, r), s) to (x, r + s), hence coincides with µ X , finishing the proof. 2 A left KZ-monad [Esc98, Definition 4.1.2, Lemma 4.1.1] (short for Kock-Zöberlein monad ) is a monad (T, η, µ)  ... 
arXiv:1707.03784v8 fatcat:vb63toh5g5ctfmu4amnayd5pfq