Completion is one of the most studied techniques in term rewriting and fundamental to automated reasoning with equalities. In this paper we present new and formalized correctness proofs of abstract completion, both for finite and infinite runs. For the special case of ground completion we present a new proof based on random descent. We moreover extend the results to ordered completion, an impor...

We apply Stone duality and model theory to study the structure theory of free pro-aperiodic monoids. Stone duality implies that elements of the free pro-aperiodic monoid may be viewed as elementary equivalence classes of pseudofinite words. Model theory provides us with saturated words in each such class, i.e., words in which all possible factorizations are realized. We give several application...

This review is meant to be an account of the properties of the infinitedimensional quantum group (specifically, Yangian) symmetry lying behind the integrability of the AdS/CFT spectral problem. In passing, the chance is taken to give a concise anthology of basic facts concerning Yangians and integrable systems, and to store a series of remarks, observations and proofs the author has collected i...

This review is meant to be an account of the properties of the infinitedimensional quantum group (specifically, Yangian) symmetry lying behind the integrability of the AdS/CFT spectral problem. In passing, the chance is taken to give a concise anthology of basic facts concerning Yangians and integrable systems, and to store a series of remarks, observations and proofs the author has collected i...

This work concerns the generation of programs which are certified to be correct byconstruction. These programs are obtained by extracting relevant information from construc-tive proofs made with the Coq proof assistant.Such a translation, named “extraction”, of constructive proofs into functional programsis not new, and corresponds to an isomorphism known as Curry-Howard’s. ...

We present some results concerning the controllability of a quasi-linear parabolic equation (with linear principal part) in a bounded domain of RN with Dirichlet boundary conditions. We analyze the controllability problem with distributed controls (supported on a small open subset) and boundary controls (supported on a small part of the boundary). We prove that the system is null and approximat...

We consider a transport equation by gradient vector field with small viscous perturbation -εΔ g . study uniform observability (resp. controllability) properties in the (singular) vanishing viscosity limit ε→0 + , that is, possibility of having uniformly bounded observation constant control cost). prove series examples general, minimal time for may be much larger than needed ε=0. also two times ...

We consider an elliptic boundary value problem with unilateral constraints and subdifferential conditions. The describes the heat transfer in a domain $D\subset\R^d$ its weak formulation is form of hemivariational inequality for temperature field, denoted by $\cP$. associate to Problem $\cP$ optimal control problem, $\cQ$. Then, using appropriate Tykhonov triples, governed nonlinear operator $G...