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The geometry of parallelism : probabilistic and quantum effects

Jeudi 2 février 11:00-12:00 - Claudia FAGGIAN - IRIF, Paris 7

The geometry of parallelism : probabilistic and quantum effects

Résumé : What become the notions of confluence and convergence when a parallel rewrite system has both a probabilistic choice and the possibility of non-termination ? We present a notion of Probabilistic Abstract Rewrite System (PARS) which deals with this issue by recovering a form of “diamond property”.
This result (the focus of the talk) is of interest in its own, but it is also key to introduce a Geometry of Interaction model for higher-order computation which has the ability to model commutative effects in a parallel setting, and to capture in particular quantum and probabilistic effects. The model (also sketched in the talk) comes with a multi-token machine, a proof net system, and a PCF-style language, which are all instances of PARS with a diamond property.
Being based on a rewrite system equipped with a memory, our model has a concrete nature which makes it well suited for building low-level operational descriptions of higher-order languages. A success of our approach is to give (essentially for free) an adequate model for a fully-fledged quantum programming language in which entanglement, duplication, and recursion are all available.
(Joint work with Ugo Dal Lago, Benoit Valiron, Akira Yoshimizu)
Référence : https://arxiv.org/pdf/1610.09629v2.pdf

JPEG - 13.7 ko
Claudia FAGGIAN

Lieu : Salle des séminaires 304-306 (3ème étage) - Institut de Mathématiques de Marseille (UMR 7373)
Site Sud
Campus de Luminy, Case 907
13288 MARSEILLE Cedex 9

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Pour en savoir plus sur cet événement, consultez l'article Séminaire Logique et Interactions