Abstract In this paper authors propose algorithms for constructing so called automaton COM(L) and prove that this automaton coincides, up to re-denoting states, with Conway’s universal automaton. We give some algorithms of constructing this automaton and consider some examples.

Abstract Anybody can make a time information authentic easily nowadays with the help of a time-stamp by a Certification Authority. In this paper, we propose a similar service for mobile devices-which have GPS receiver-to authentication GPS coordinates. This service name is location-stamping, and we propose two protocols for this service.

Abstract A double-sided shadow minimization problem in the Boolean cube layer is investigated in this paper. The problem is to minimize the size of the union of the lower and upper shadows of a k-uniform family of subsets of [n]. It is shown that if 3 ⋜ k ⋜ n−3, there is no total order such that all its initial segments have minimal double-sided shadow.