The robustness of the famous compression algorithm of Lempel and Ziv is still not well understood: in particular, until now it was unknown whether the addition of one bit in front of a compressible word could make it incompressible. This talk will answer that question, advertised by Jack Lutz under the name “one-bit catastrophe” and which has been around since at least 1998. We will show that a “well” compressible word remains compressible when a bit is added in front of it, but some “few” compressible words indeed become incompressible. This is a joint work with Guillaume Lagarde.

Numerous contributions have been made for some years to allow users to exchange formal proofs between different provers. The main propositions consist in ad hoc pointwise translations, e.g. between HOL Light and Isabelle in the Flyspeck project or uses of more or less complete certificates. We propose a methodology to combine proofs coming from different theorem provers. This methodology relies on the Dedukti logical framework as a common formalism in which proofs can be translated and combined. To relate the independently developed mathematical libraries used in proof assistants, we rely on the structuring features offered by FoCaLiZe, in particular parameterized modules and inheritance to build a formal library of transfer theorems called MathTransfer. We finally illustrate this methodology on the Sieve of Eratosthenes, which we prove correct using HOL and Coq in combination.

This special session will introduce three new PhD students who will each be giving a short talk.

TBA