Ilias Garnier

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We provide an overview of the FET-Open Project CerCo (‘Certified Complexity’). Our main achievement is the development of a technique for analysing non-functional properties of programs (time, space) at the source level with little or no loss of accuracy and a small trusted code base. The core component is a C compiler, verified in Matita, that produces an(More)
Bulk-Synchronous Parallel ML (BSML) is a ML based language to code Bulk-Synchronous Parallel (BSP)<lb>algorithms. It allows an estimation of execution time, avoids deadlocks and non-determinism. BSML proposes an<lb>extension of ML programming with parallel primitives on a parallel data structure called parallel vector. One of<lb>these primitives is(More)
BSML is a ML based language designed to code Bulk Synchronous Parallel (BSP) algorithms. It allows an estimation of execution time, avoids deadlocks and non-determinism. BSML proposes an extension of ML programming with a small set of primitives. One of these primitives, called parallel superposition, allows the parallel composition of two BSP programs.(More)
Giry and Lawvere’s categorical treatment of probabilities, based on the probabilistic monad G, offer an elegant and hitherto unexploited treatment of higher-order probabilities. The goal of this paper is to follow this formulation to reconstruct a family of higher-order probabilities known as the Dirichlet process. This family is widely used in(More)
BSML is an ML based language designed to code Bulk Synchronous Parallel (BSP) algorithms. It allows an estimation of execution time, avoids deadlocks and non-determinism. BSML proposes an extension of ML programming with a small set of primitives. One of these primitives, called parallel superposition, allows the parallel composition of two BSP programs.(More)
We present a method for constructing robustly parameterised families of higher-order probabilistic models. Parameter spaces and models are represented by certain classes of functors in the category of Polish spaces. Maps from parameter spaces to models (parameterisations) are continuous and natural transformations between such functors. Naturality ensures(More)
This paper presents an investigation of the notion of reaction time in some synchronous systems. A state-based description of such systems is given, and the reaction time of such systems under some classic composition primitives is studied. Reaction time is shown to be non-compositional in general. Possible solutions are proposed, and applications to(More)
The process of inverting Markov kernels relates to the important subject of Bayesian modelling and learning. In fact, Bayesian update is exactly kernel inversion. In this paper, we investigate how and when Markov kernels (aka stochastic relations, or probabilistic mappings, or simply kernels) can be inverted. We address the question both directly on the(More)