Séminaire, 13 novembre 2014
Programme
 10:30 – 12:00

Dimitri Ara (Univ AixMarseille)Invited talk: Street's orientals and Mac Lane's coherence theorem
In this talk, I will present some elements of the homotopy theory of strict ncategories, insisting on Street's orientals. The nth oriental is a strict ncategory shaped on the nsimplex. We will see that these objects govern higher associativities and in particular that Mac Lane's coherence theorem can be rephrased in terms of the combinatorics of low dimensional orientals. Using this setting and homotopical methods, I will sketch a proof of Mac Lane's coherence theorem. (This talk is based on joint work with Georges Maltsiniotis.)
 14:00 – 15:00

Lucca Hirschi (ENS Cachan)Invited talk: Partial order reduction for the applied picalculus
Process algebras provide convenient languages for representing concurrent computation, and they have been used successfully to model complex systems such as security protocols. However, their naive interleaving semantics gives rise to exponentially many states that are essentially the same. This is problematic, for instance, when modelchecking security protocols. We solve this problem on a large fragment of the applied picalculus by providing reduced transition systems that optimally eliminate redundant traces, and which are still adequate for onthefly modelchecking of reachability and (in the actiondeterministic case) trace equivalence properties.
Technically, we rely on basic trace theory but also on focusing from proof theory.
(Joint work with Baelde & Delaune.)
 15:30 – 16:30

JeanBaptiste Jeannin (Carnegie Mellon University)Invited talk: Semantic Foundations for Networks
Recent years have seen growing interest in highlevel languages for programming networks. But the design of these languages has been largely ad hoc, driven more by the needs of applications and the capabilities of network hardware than by foundational principles. The lack of a semantic foundation has left language designers with little guidance in determining how to incorporate new features, and programmers without a means to reason precisely about their code.
In this talk we introduce NetKAT, a new network programming language that is based on a solid mathematical foundation and comes equipped with a sound and complete equational theory. We describe the design of NetKAT, including primitives for filtering, modifying, and transmitting packets; union and sequential composition operators; and a Kleene star operator that iterates programs. We show that NetKAT is an instance of a canonical and wellstudied mathematical structure called a Kleene algebra with tests KAT and prove that its equational theory is sound and complete with respect to its denotational semantics. Finally, we present practical applications of the equational theory including syntactic techniques for checking reachability, proving noninterference properties that ensure isolation between programs, and establishing the correctness of compilation algorithms.