{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,24]],"date-time":"2025-08-24T01:35:14Z","timestamp":1755999314339,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2019,3,29]],"date-time":"2019-03-29T00:00:00Z","timestamp":1553817600000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,3,29]],"date-time":"2019-03-29T00:00:00Z","timestamp":1553817600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,3,29]],"date-time":"2019-03-29T00:00:00Z","timestamp":1553817600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"crossref","award":["DP120101413"],"award-info":[{"award-number":["DP120101413"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>Hidden Markov Models, HMM's, are mathematical models of Markov processes with state that is hidden, but from which information can leak. They are typically represented as 3-way joint-probability distributions.   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 $\\mathbb{D}$, and we equip them with a partial order of increasing security. However to encode the monadic type with hiding over some state $\\mathcal{X}$ we use $\\mathbb{D}\\mathcal{X}\\to \\mathbb{D}^2\\mathcal{X}$ rather than the conventional $\\mathcal{X}{\\to}\\mathbb{D}\\mathcal{X}$ that suffices for Markov models whose state is not hidden. We illustrate the $\\mathbb{D}\\mathcal{X}\\to \\mathbb{D}^2\\mathcal{X}$ construction with a small Haskell prototype.   We then present uncertainty measures as a generalisation of the extant diversity of probabilistic entropies, with characteristic analytic properties for them, and show how the new entropies interact with the order of increasing security. Furthermore, we give a `backwards' uncertainty-transformer semantics for HMM's that is dual to the `forwards' abstract HMM's - it is an analogue of the duality between forwards, relational semantics and backwards, predicate-transformer semantics for imperative programs with demonic choice.   Finally, we argue that, from this new denotational-semantic viewpoint, one can see that the Dalenius desideratum for statistical databases is actually an issue in compositionality. We propose a means for taking it into account.<\/jats:p>","DOI":"10.23638\/lmcs-15(1:36)2019","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:34:14Z","timestamp":1743701654000},"source":"Crossref","is-referenced-by-count":1,"title":["Abstract Hidden Markov Models: a monadic account of quantitative information flow"],"prefix":"10.23638","volume":"Volume 15, Issue 1","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2405-9838","authenticated-orcid":false,"given":"Annabelle","family":"McIver","sequence":"first","affiliation":[]},{"given":"Carroll","family":"Morgan","sequence":"additional","affiliation":[]},{"given":"Tahiry","family":"Rabehaja","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2019,3,29]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1708.01688v3","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1708.01688v3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:34:14Z","timestamp":1743701654000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/3851"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,29]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-15(1:36)2019","relation":{"has-preprint":[{"id-type":"arxiv","id":"1708.01688v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1708.01688v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1708.01688","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1708.01688","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2019,3,29]]},"article-number":"3851"}}