Related papers: The Importance of the Algorithmic Information Theo…
In this short communication it is proposed the general form of a n-qubit disentangled state as a irreducible sentence, in the sense explained by the algorithmic information theory, whose length increases in a non-polynomial way when the…
In this short communication, it is shown a simple problem using quantum circuits for which the algorithmic information theory guarantee that the minimal length of the algorithm able to solve it grows exponentially with the number of qubits.
In this work, are used Chaitin number Omega and the fact that the general decomposition of an N-way disentangled state is an irreducible sentence whose number of coefficients grows in a non-polynomial way with N, to construct a problem that…
Quantum information theory is used to analize various non-linear operations on quantum states. The universal disentanglement machine is shown to be impossible, and partial (negative) results are obtained in the state-dependent case. The…
The current state-of-the-art in artificial intelligence is impressive, especially in terms of mastery of language, but not so much in terms of mathematical reasoning. What could be missing? Can we learn something useful about that gap from…
This paper applies Algorithmic Information Theory to simple examples of replication processes to illustrate how replicating structures can generate and maintain order in a non equilibrium system. Variation in replicating structures enhances…
Algorithmic statistics considers the following problem: given a binary string $x$ (e.g., some experimental data), find a "good" explanation of this data. It uses algorithmic information theory to define formally what is a good explanation.…
This note is intended to foster a discussion about the extent to which typical problems arising in quantum information theory are algorithmically decidable (in principle rather than in practice). Various problems in the context of…
Learning disentangled representations of natural language is essential for many NLP tasks, e.g., conditional text generation, style transfer, personalized dialogue systems, etc. Similar problems have been studied extensively for other forms…
The paper elaborates an endeavor on applying the algorithmic information-theoretic computational complexity to meta-social-sciences. It is motivated by the effort on seeking the impact of the well-known incompleteness theorem to the…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
The data augmentation (DA) algorithm is a simple and powerful tool in statistical computing. In this note basic information theory is used to prove a nontrivial convergence theorem for the DA algorithm.
I will survey some matters of relevance to a philosophical discussion of information, taking into account developments in algorithmic information theory (AIT). I will propose that meaning is deep in the sense of Bennett's logical depth, and…
Algorithmic information theory roots the concept of information in computation rather than probability. These lecture notes were constructed in conjunction with the graduate course I taught at Universit\`a della Svizzera italiana in the…
Probabilistic epistemic argumentation allows for reasoning about argumentation problems in a way that is well founded by probability theory. Epistemic states are represented by probability functions over possible worlds and can be adjusted…
Information theory is a mathematical theory of learning with deep connections with topics as diverse as artificial intelligence, statistical physics, and biological evolution. Many primers on information theory paint a broad picture with…
The act of telling stories is a fundamental part of what it means to be human. This work introduces the concept of narrative information, which we define to be the overlap in information space between a story and the items that compose the…
We introduce the notions of algorithmic mutual information and rarity of quantum states. These definitions enjoy conservation inequalities over unitary transformations and partial traces. We show that a large majority of pure states have…
What would be the consequences if there were fundamental limits to our ability to experimentally explore the world? In this work we seriously consider this question. We assume the existence of statements whose truth value is not…
We show that the conservation and the non-additivity of the information, together with the additivity of the entropy make the entropy increase in an isolated system. The collapse of the entangled quantum state offers an example of the…