Several Galerkin schemes for approximate solution of linear elliptic boundary value problems are studied for such computational aspects as obtainable accuracy, sensitivity to parameters and conditioning of linear systems. Methods studied involve computing subspaces (e.g., splines) whose elements need not satisfy boundary conditions. A Poisson problem study on the square produces computed error ...

We develop a Tanner graph (TG) construction for an Abelian group block code with arbitrary alphabets at different coordinates, an important application of which is the representation of the label code of a lattice. The construction is based on the modular linear constraints imposed on the code symbols by a set of generators for the dual code . As a necessary step toward the construction of a TG...

Below is a translation from my Russian paper. I added references, unavailable to me in Moscow. Similar results have been also given in [Schnorr Stumpf 75] (see also [Lynch 75]). Earlier relevant work (classical theorems like Compression, Speed-up, etc.) was done in [Tseitin 56, Rabin 59, Hartmanis Stearns 65, Blum 67, Trakhtenbrot 67, Meyer Fischer 72]. I translated only the part with the state...

This paper consider the problem of generating symmetry-breaking formulas for permutation groups acting on n points, where the projection of the group into each orbit is bounded by a polynomial in n. We show that the lex-leader formula, which is satisfied by the lexicographic leader of each set of symmetrical points in the search space, can be generated in polynomial time (and space). Our constr...

In this paper we propose two compilers which are designed to transform a group key exchange protocol secure against any passive adversary into an authenticated group key exchange protocol with key confirmation which is secure against any passive adversary, active adversary, or malicious insider. We show that the first proposed compiler gives protocols that are more efficient than those produced...

&bstract. The use of symmetry to alleviate state-explosion problems during model-checking has become a important research topic. This paper investigates several problems which are important to techniques exploiting symmetry. The most important of these problems is the orbit problem. We prove that the orbit problem is equivalent to an important problem in computational group theory which is at l...