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Main Author:	Neves, Renato
Format:	Preprint
Published:	2024
Subjects:	Logic in Computer Science
Online Access:	https://arxiv.org/abs/2409.15920
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author	Neves, Renato
author_facet	Neves, Renato
contents	We present an adequacy theorem for a concurrent extension of probabilistic GCL. The underlying denotational semantics is based on the so-called mixed powerdomains, which combine non-determinism with probabilistic behaviour. The theorem itself is formulated via M. Smyth's idea of treating observable properties as open sets of a topological space. The proof hinges on a 'topological generalisation' of König's lemma in the setting of probabilistic programming (a result that is proved in the paper as well). One application of the theorem is that it entails semi-decidability w.r.t. whether a concurrent program satisfies an observable property (written in a certain form). This is related to M. Escardó's conjecture about semi-decidability w.r.t. may and must probabilistic testing.
format	Preprint
id	arxiv_https___arxiv_org_abs_2409_15920
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	An adequacy theorem between mixed powerdomains and probabilistic concurrency (extended version) Neves, Renato Logic in Computer Science We present an adequacy theorem for a concurrent extension of probabilistic GCL. The underlying denotational semantics is based on the so-called mixed powerdomains, which combine non-determinism with probabilistic behaviour. The theorem itself is formulated via M. Smyth's idea of treating observable properties as open sets of a topological space. The proof hinges on a 'topological generalisation' of König's lemma in the setting of probabilistic programming (a result that is proved in the paper as well). One application of the theorem is that it entails semi-decidability w.r.t. whether a concurrent program satisfies an observable property (written in a certain form). This is related to M. Escardó's conjecture about semi-decidability w.r.t. may and must probabilistic testing.
title	An adequacy theorem between mixed powerdomains and probabilistic concurrency (extended version)
topic	Logic in Computer Science
url	https://arxiv.org/abs/2409.15920

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// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

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