Séminaire, Nov. 13, 2014


10:30 – 12:00
Dimitri Ara (Univ Aix-Marseille)

In this talk, I will present some elements of the homotopy theory of strict n-categories, insisting on Street's orientals. The n-th oriental is a strict n-category shaped on the n-simplex. 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)

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 model-checking security protocols. We solve this problem on a large fragment of the applied pi-calculus by providing reduced transition systems that optimally eliminate redundant traces, and which are still adequate for on-the-fly model-checking of reachability and (in the action-deterministic 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
Jean-Baptiste Jeannin (Carnegie Mellon University)

Recent years have seen growing interest in high-level 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 well-studied 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 non-interference properties that ensure isolation between programs, and establishing the correctness of compilation algorithms.