20 citations · 70 across the 12 of their papers we have counts for
5 papers · 1 filter
A constructive version of Birkhoff's ergodic theorem for Martin-Löf random points
Laurent Bienvenu, Adam Day, Mathieu Hoyrup +2
A theorem of Kučera states that given a Martin-Löf random infinite binary sequence ω and an effectively open set A of measure less than 1, some tail of ω is not in A. We first prov…
Insuring against loss of evidence in game-theoretic probability
A. Philip Dawid, Steven de Rooij, Glenn Shafer +3
We consider the game-theoretic scenario of testing the performance of Forecaster by Sceptic who gambles against the forecasts. Sceptic's current capital is interpreted as the amoun…
Game interpretation of Kolmogorov complexity
Andrej A. Muchnik, Ilya Mezhirov, Alexander Shen +1
The Kolmogorov complexity function K can be relativized using any oracle A, and most properties of K remain true for relativized versions. In section 1 we provide an explanation fo…
Effective closed subshifts in 1D can be implemented in 2D
Bruno Durand, Andrei Romashchenko, Alexander Shen
In this paper we use fixed point tilings to answer a question posed by Michael Hochman and show that every one-dimensional effectively closed subshift can be implemented by a local…
Fixed point theorem and aperiodic tilings
Bruno Durand, Andrei Romashchenko, Alexander Shen
We propose a new simple construction of an aperiodic tile set based on self-referential (fixed point) argument. People often say about some discovery that it appeared "ahead of tim…