We survey some results related to classical secret sharing schemes defined in Shamir [10] and Blakley [1], and developed in Brickell [2] and Lai and Ding [4]. Using elementary symmetric polynomials, we describe in a unified way which allocations of i

In this paper we pursue the propositional calculus and the SATisfiability solvers as a powerful declarative programming environment that makes it possible to create and run the propositional declarative programs for computational tasks in various areas of mathematics. We report some experimental results on our application of the propositional SATisfiability environment to computing some simple orthogonal matrices and the orders of some orthogonal groups. Some encouraging (and not very encouraging) experiments are reported for the proposed propositional search procedures using off-the-shelf general-purpose SAT solvers. Our new software toolkit SAT4Alg is announced.

We consider first-order specifications together with the restriction to accept only programmable algebras as models. We provide a criterion which links this approach with the "generation principle": all programmable models of any specification SP that meets this criterion are reachable. We also show an example of a specification which does not satisfy the criterion and admits a programmable yet nonreachable model. Moreover, a general method of showing the existence of programmable but nonreachable models for a class of first-order specifications is given.