We consider here the Byzantine Agreement problem (BA) in synchronous systems with homonyms in the case where some identifiers may be forgeable. More precisely, the n processes share a set of l (1 ≤ l ≤ n) identifiers. Assuming that at most t processes may be Byzantine and at most k (t ≤ k ≤ l) of these identifiers are forgeable in the sense that any Byzantine process can falsely use them, we pr...

let $g$ be a finite group‎. ‎a subgroup‎ ‎$h$ of $g$ is called an $mathcal h $ -subgroup in‎ ‎$g$ if $n_g (h)cap h^gleq h$ for all $gin‎ ‎g$. a subgroup $h$ of $g$ is called a weakly‎ $mathcal h^ast $-subgroup in $g$ if there exists a‎ ‎subgroup $k$ of $g$ such that $g=hk$ and $hcap‎ ‎k$ is an $mathcal h$-subgroup in $g$. we‎ ‎investigate the structure of the finite group $g$ under the‎ ‎assump...

When studying non-linear (higher order MUSCL type) nite volume approximation of a linear convection diiusion problem, one is confronted with a question whether the corresponding nonlinear discrete problem is solvable. In this contribution we note that the corresponding discrete problem L h u h = f h in two dimensions in general need not to possess a solution. However, we show that to every righ...

We present a deterministic, log-space algorithm that solves st-connectivity in undirected graphs. The previous bound on the space complexity of undirected st-connectivity was log(·) obtained by Armoni, Ta-Shma, Wigderson and Zhou [ATSWZ00]. As undirected st-connectivity is complete for the class of problems solvable by symmetric, non-deterministic, log-space computations (the class SL), this al...

We show that there is a field F complete with respect to a discrete valuation whose residue field is perfect and there is a finite Galois extension K|F such that there is no solvable Galois extension L|F such that the extension KL|K is unramified, where KL is the composite of K and L. As an application we deduce that that there is a field F as above and there is a smooth, projective, geometrica...

We present a deterministic, log-space algorithm that solves st-connectivity in undirected graphs. The previous bound on the space complexity of undirected st-connectivity was log(·) obtained by Armoni, Ta-Shma, Wigderson and Zhou [ATSWZ00]. As undirected st-connectivity is complete for the class of problems solvable by symmetric, non-deterministic, log-space computations (the class SL), this al...

We prove a variant of the well-known Reidemeister-Schreier Theorem for finitely L-presented groups. More precisely, we prove that each finite index subgroup of a finitely L-presented group is itself finitely L-presented. Our proof is constructive and it yields a finite L-presentation for the subgroup. We further study conditions on a finite index subgroup of an invariantly finitely L-presented ...

We study the half-integral k-Directed Disjoint Paths Problem ( 2kDDPP) in highly strongly connected digraphs. The integral kDDPP is NP-complete even when restricted to instances where k = 2, and the input graph is L-strongly connected, for any L ≥ 1. We show that when the integrality condition is relaxed to allow each vertex to be used in two paths, the problem becomes efficiently solvable in h...

By exploiting an old idea first used by Pizzetti for the classical Laplacian, we introduce a notion of asymptotic average solutions making pointwise solvable every Poisson equation ${\mathcal {L}} u(x)=-f(x)$ with continuous data f, where {L}}$ is hypoelliptic linear partial differential operator positive semidefinite characteristic form.