Computability and complexity in analysis : 4th international workshop, CCA 2000, Swansea, UK, September 17-19, 2000, selected papers

viii, 393 p. : ill. ; 24 cm

Computable de Finetti measures

We prove a computable version of de Finetti's theorem on exchangeable sequences of real random variables. As a consequence, exchangeable stochastic processes expressed in probabilistic functional programming languages can be automatically rewritten as procedures that do not modify non-local state. Along the way, we prove that a distribution on the unit interval is computable if and only if its moments are uniformly computable.Comment: 32 pages. Final journal version; expanded somewhat, with minor corrections. To appear in Annals of Pure and Applied Logic. Extended abstract appeared in Proceedings of CiE '09, LNCS 5635, pp. 218-23

Unexpected distribution phenomenon resulting from Cantor series expansions

We explore in depth the number theoretic and statistical properties of certain sets of numbers arising from their Cantor series expansions. As a direct consequence of our main theorem we deduce numerous new results as well as strengthen known ones.Comment: 32 page