Christine Tasson
Paris Diderot University
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Publication
Featured researches published by Christine Tasson.
symposium on principles of programming languages | 2014
Thomas Ehrhard; Christine Tasson; Michele Pagani
Probabilistic coherence spaces (PCoh) yield a semantics of higher-order probabilistic computation, interpreting types as convex sets and programs as power series. We prove that the equality of interpretations in Pcoh characterizes the operational indistinguishability of programs in PCF with a random primitive. This is the first result of full abstraction for a semantics of probabilistic PCF. The key ingredient relies on the regularity of power series. Along the way to the theorem, we design a weighted intersection type assignment system giving a logical presentation of PCoh.
logic in computer science | 2011
Thomas Ehrhard; Michele Pagani; Christine Tasson
We study the probabilistic coherent spaces -- a denotational semantics interpreting programs by power series with non negative real coefficients. We prove that this semantics is adequate for a probabilistic extension of the untyped
symposium on the theory of computing | 2014
Hammurabi Mendes; Christine Tasson; Maurice Herlihy
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Logical Methods in Computer Science | 2014
Ali Assaf; Alejandro Díaz-Caro; Simon Perdrix; Christine Tasson; Benoî t Valiron
-calculus: the probability that a term reduces to ahead normal form is equal to its denotation computed on a suitable set of values. The result gives, in a probabilistic setting, a quantitative refinement to the adequacy of Scotts model for untyped
Applied Categorical Structures | 2015
Eric Goubault; Samuel Mimram; Christine Tasson
\lambda
international conference on typed lambda calculi and applications | 2009
Christine Tasson
-calculus.
Journal of the ACM | 2018
Thomas Ehrhard; Michele Pagani; Christine Tasson
In this work, we extend the topology-based approach for characterizing computability in asynchronous crash-failure distributed systems to asynchronous Byzantine systems. We give the first theorem with necessary and sufficient conditions to solve arbitrary tasks in asynchronous Byzantine systems where an adversary chooses faulty processes. For colorless tasks, an important subclass of distributed problems, the general result reduces to an elegant model that effectively captures the relation between the number of processes, the number of failures, as well as the topological structure of the tasks simplicial complexes.
Mathematical Structures in Computer Science | 2016
Christine Tasson; Lionel Vaux
We examine the relationship between the algebraic lambda-calculus, a fragment of the differential lambda-calculus and the linear-algebraic lambda-calculus, a candidate lambda-calculus for quantum computation. Both calculi are algebraic: each one is equipped with an additive and a scalar-multiplicative structure, and their set of terms is closed under linear combinations. However, the two languages were built using different approaches: the former is a call-by-name language whereas the latter is call-by-value; the former considers algebraic equalities whereas the latter approaches them through rewrite rules. In this paper, we analyse how these different approaches relate to one another. To this end, we propose four canonical languages based on each of the possible choices: call-by-name versus call-by-value, algebraic equality versus algebraic rewriting. We show that the various languages simulate one another. Due to subtle interaction between beta-reduction and algebraic rewriting, to make the languages consistent some additional hypotheses such as confluence or normalisation might be required. We carefully devise the required properties for each proof, making them general enough to be valid for any sub-language satisfying the corresponding properties.
foundations of software science and computation structure | 2017
Raphaëlle Crubillé; Thomas Ehrhard; Michele Pagani; Christine Tasson
The standard chromatic subdivision of the standard simplex is a combinatorial algebraic construction, which was introduced in theoretical distributed computing, motivated by the study of the view complex of layered immediate snapshot protocols. A most important property of this construction is the fact that the iterated subdivision of the standard simplex is contractible, implying impossibility results in fault-tolerant distributed computing. Here, we prove this result in a purely combinatorial way, by showing that it is collapsible, studying along the way fundamental combinatorial structures present in the category of colored simplicial complexes.
Distributed Computing | 2018
Eric Goubault; Samuel Mimram; Christine Tasson
Finiteness spaces constitute a categorical model of Linear Logic (LL) whose objects can be seen as linearly topologised spaces, (a class of topological vector spaces introduced by Lefschetz in 1942) and morphisms as continuous linear maps. First, we recall definitions of finiteness spaces and describe their basic properties deduced from the general theory of linearly topologised spaces. Then we give an interpretation of LL based on linear algebra. Second, thanks to separation properties, we can introduce an algebraic notion of totality candidate in the framework of linearly topologised spaces: a totality candidate is a closed affine subspace which does not contain 0. We show that finiteness spaces with totality candidates constitute a model of classical LL. Finally, we give a barycentric simply typed lambda-calculus, with booleans