20 citations · 56 across the 31 of their papers we have counts for
5 papers · 1 filter
Monotonous betting strategies in warped casinos
George Barmpalias, Nan Fang, Andrew Lewis-Pye
Suppose that the outcomes of a roulette table are not entirely random, in the sense that there exists a successful betting strategy. Is there a successful `separable' strategy, in…
Limits of the Kucera-Gacs coding method
George Barmpalias, Andrew Lewis-Pye
Every real is computable from a Martin-Loef random real. This well known result in algorithmic randomness was proved by Kucera and Gacs. In this survey article we discuss various a…
A note on the differences of computably enumerable reals
George Barmpalias, Andrew Lewis-Pye
We show that given any non-computable left-c.e. real there exists a left-c.e. real such that for all left-c.e. reals and all right-c.e. reals . The proof is…
Optimal asymptotic bounds on the oracle use in computations from Chaitin's Omega
George Barmpalias, Nan Fang, Andrew Lewis-Pye
Chaitin's number Omega is the halting probability of a universal prefix-free machine, and although it depends on the underlying enumeration of prefix-free machines, it is always Tu…
The typical Turing degree
George Barmpalias, Adam R. Day, Andrew E. M. Lewis
The Turing degree of a real measures the computational difficulty of producing its binary expansion. Since Turing degrees are tailsets, it follows from Kolmogorov's 0-1 law that fo…