6 papers · 1 filter
On Kolmogorov Structure Functions
Samuel Epstein
All strings with low mutual information with the halting sequence will have flat Kolmogorov Structure Functions, in the context of Algorithmic Statistics. Assuming the Independence…
Semi-Classical Subspaces, The No Synchronization Law, and More
Samuel Epstein
This paper looks at the intersection of algorithmic information theory and physics, namely quantum mechanics, thermodynamics, and black holes. We discuss theorems which characteriz…
Game Derandomization
Samuel Epstein
Using Kolmogorov Game Derandomization, upper bounds of the Kolmogorov complexity of deterministic winning players against deterministic environments can be proved. This paper gives…
Two Quantum Paradigms, but Still No Signal
Samuel Epstein
An overwhelming majority of quantum (pure and mixed) states, when undertaking a POVM measurement, will result in a classical probability with no algorithmic information. Thus most…
Two Simple Proofs of Müller's Theorem
Samuel Epstein
Due to Müller's theorem, the Kolmogorov complexity of a string was shown to be equal to its quantum Kolmogorov complexity. Thus there are no benefits to using quantum mechanics to…
The Randomness Deficiency Function and the Shift Operator
Samuel Epstein
Almost surely, the difference between the randomness deficiencies of two infinite sequences will be unbounded with respect to repeated iterations of the shift operator.