Eigenring and Reducibility of Difference Equations

Reducibility and Stability Results for Linear System of Difference Equations

Reducibility of linear equations with quasi-periodic coefficients. A survey

Preface This survey deals with some aspects of the problem of reducibility for linear equations with quasi-periodic coefficients. It is a compilation of results on this problem, some already classical and some other more recent. Our motivation comes from the study of stability of quasi-periodic motions and preservation of invariant tori in Hamiltonian mechanics (where the reducibility of linear...

Boundary charges in gauge theories: using Stokes theorem in the bulk

Boundary charges in gauge theories (like the ADM mass in general relativity) can be understood as integrals of linear conserved n-2 forms of the free theory linearized around the background. These forms are associated one-to-one to reducibility parameters of this background (like the time-like Killing vector of Minkowski space-time). For such n-2 forms, a non-linear completion is constructed th...

Some Reducibility Properties for Pseudovarieties of the Form Drh

Let H be a pseudovariety of groups and DRH be the pseudovariety containing all finite semigroups whose regular R-classes belong to H. We study the relationship between reducibility of H and of DRH with respect to several particular classes of systems of equations. The classes of systems considered (of pointlike, idempotent pointlike and graph equations) are known to play a role in decidability ...

On truth-table reducibility to SAT and the difference hierarchy over NP

We show that polynomial time truth-table reducibility via Boolean circuits to SAT is the same as log space truth-table reducibility via Boolean formulas to SAT and the same as log space Turing reducibility to SAT. In addition, we prove that a constant number of rounds of parallel queries to SAT is equivalent to one round of parallel queries. Finally, we show that the infinite difference hierarc...