If you search a sequence database for homologs of a structural RNA, you don’t want to search just for linear sequence similarity; you alsowant the search program to consider whether a candidate sequence can be folded into a similar base-paired secondary structure. A powerful and general class of computational methods for combining primary sequence and secondary structure information in RNA homo...

In this paper a practical methodology for formally verifying RISC cores is presented. Using a hierarchical model which reflects the abstraction levels used by designers of real RISC processors, proofs between neighboring levels are performed for simplifying the verification process. The proofs are performed by showing that each instruction is executed correctly by the pipelined machine with res...

This thesis aims at exploring the scopes and limits of techniques for extracting programs from proofs. We focus on constructive theories of inductive definitions and classical systems allowing choice principles. Special emphasis is put on optimizations that allow for the extraction of realistic programs. Our main field of application is infinitary combinatorics. Higman’s Lemma, having an elegan...

To ensure the privacy of users in transport systems, researchers are working on new protocols providing the best security guarantees while respecting functional requirements of transport operators. In this paper , we design a secure NFC m-ticketing protocol for public transport that preserves users’ anonymity and prevents transport operators from tracing their customers’ trips. To this end, we ...

Proof reconstruction is a technique that combines an interactive theorem prover and an automatic one in a sound way, so that users benefit from the expressiveness of the first tool and the automation of the latter. We present an implementation of proof reconstruction for first-order logic and set-theoretical constructions between the interactive theorem prover Isabelle and the automatic SMT pro...

The attempt to mechanize mathematical reasoning belongs to the first experiments in artificial intelligence in the 1950 (Newell et al., 1957). However, the idea to automate or to support deduction turned out to be harder than originally expected. This can not at least be seen in the multitude of approaches that were pursued to model different aspects of mathematical reasoning. There are differe...

Gradient descent noise reduction is a technique that attempts to recover the true signal, or trajectory, from noisy observations of a non-linear dynamical system for which the dynamics are known. This paper provides the first rigorous proof that the algorithm will recover the original trajectory for a broad class of dynamical systems under certain conditions. The proof is obtained using ideas f...

For a public value y and a linear function f , giving a zero-knowledge proof of knowledge of a secret value x that satisfies f(x) = y is a key ingredient in many cryptographic protocols. Lattice-based constructions, in addition, require proofs of “shortness” of x. Of particular interest are constructions where f is a function over polynomial rings, since these are the ones that result in effici...