16 citations · 54 across the 28 of their papers we have counts for
33 papers
Characterizing normality via automata and random matrix products
Laurent Bienvenu, Santiago Cifuentes, Hugo Gimbert
For a fixed alphabet A, an infinite sequence X is said to be normal if every word w over A appears in X with the same frequency as any other word of the same length. A classical re…
Probabilistic vs deterministic gamblers
Laurent Bienvenu, Valentino Delle Rose, Tomasz Steifer
Can a probabilistic gambler get arbitrarily rich when all deterministic gamblers fail? We study this problem in the context of algorithmic randomness, introducing a new notion -- a…
Relativized depth
Laurent Bienvenu, Valentino Delle Rose, Wolfgang Merkle
Bennett's notion of depth is usually considered to describe the usefulness and internal organization of the information encoded into an object such as an infinite binary sequence.…
Some Questions of Uniformity in Algorithmic Randomness
Laurent Bienvenu, Barbara Csima, Matthew Harrison-Trainor
The numbers-the halting probabilities of universal prefix-free machines-are known to be exactly the Martin-L{ö}f random left-c.e. reals. We show that one cannot uniformly produ…
Bad oracles in higher computability and randomness
Laurent Bienvenu, Noam Greenberg, Benoit Monin
Many constructions in computability theory rely on "time tricks". In the higher setting, relativising to some oracles shows the necessity of these. We construct an oracle~ and a…
Optimal bounds for single-source Kolmogorov extractors
Laurent Bienvenu, Barbara F. Csima, Matthew Harrison-Trainor
The rate of randomness (or dimension) of a string is the ratio where is the Kolmogorov complexity of . While it is known that a single computable transform…