Non-Archimedean Ergodic Theory and Pseudorandom Generators
The paper develops techniques in order to construct computer programs, pseudorandom number generators (PRNG), that produce uniformly distributed sequences. The paper exploits an approach that treats standard processor instructions (arithmetic and bitwise logical ones) as continuous functions on the space of 2-adic integers. Within this approach, a PRNG is considered as a dynamical system and is studied by means of the non-Archimedean ergodic theory.
pseudorandom generator uniformly distributed sequence non-archimedean analysis ergodic function measure-preserving function balanced mapping