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09/08/2023
### The Randomness Deficiency Function and the Shift Operator

Almost surely, the difference between the randomness deficiencies of two...
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04/16/2023
### Regression and Algorithmic Information Theory

In this paper we prove a theorem about regression, in that the shortest ...
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03/13/2023
### On the Algorithmic Information Between Probabilities

We extend algorithmic conservation inequalities to probability measures....
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03/11/2023
### A Quantum Outlier Theorem

In recent results, it has been proven that all sampling methods produce ...
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03/09/2023
### Uniform Tests and Algorithmic Thermodynamic Entropy

We prove that given a computable metric space and two computable measure...
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03/09/2023
### How to Compress the Solution

Using derandomization, we provide an upper bound on the compression size...
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03/09/2023
### On the Existence of Anomalies, The Reals Case

The Independence Postulate (IP) is a finitary Church-Turing Thesis, sayi...
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02/14/2023
### A Complication for the Many Worlds Theory

The Many Worlds Theory and the Independence Postulate are in conflict, a...
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02/12/2023
### On the Existence of Anomalies

The Independence Postulate (IP) is a finitary Church-Turing Thesis, sayi...
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01/19/2023
### A Quantum EL Theorem

In this paper, we prove a quantum version of the EL Theorem. It states t...
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11/26/2022
### Derandomization under Different Resource Constraints

We provide another proof to the EL Theorem. We show the tradeoff between...
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08/24/2022
### 22 Examples of Solution Compression via Derandomization

We provide bounds on the compression size of the solutions to 22 problem...
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08/24/2022
### The Kolmogorov Birthday Paradox

We prove a Kolmogorov complexity variant of the birthday paradox. Suffic...
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07/08/2022
### Outliers, Dynamics, and the Independence Postulate

We show that outliers occur almost surely in computable dynamics over in...
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03/16/2022
### The Outlier Theorem Revisited

An outlier is a datapoint that is set apart from a sample population. Th...
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01/28/2022
### On the Kolmogorov Complexity of Binary Classifiers

We provide tight upper and lower bounds on the expected minimum Kolmogor...
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02/07/2021
### On the Algorithmic Content of Quantum Measurements

We show that given a quantum measurement, for an overwhelming majority o...
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01/29/2020
### Approximations of Kolmogorov Complexity

In this paper we show that the approximating the Kolmogorov complexity o...
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07/10/2019
### On the Algorithmic Probability of Sets

The combined universal probability m(D) of strings x in sets D is close ...
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07/10/2019
### On the Complexity of Completing Binary Predicates

Given a binary predicate P, the length of the smallest program that comp...
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07/01/2019
### Information Kernels

Given a set X of finite strings, one interesting question to ask is whet...
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08/09/2018
### Algorithmic No-Cloning Theorem

We introduce the notions of algorithmic mutual information and rarity of...
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07/05/2011