相关论文: An Invitation to Algorithmic Information Theory

The latest in a series of reports presenting the information-theoretic incompleteness theorems of algorithmic information theory via algorithms written in specially designed versions of LISP. Previously in this LISP code only one-character…

This is an alternative version of the course notes in chao-dyn/9407003. The previous version is based on measuring the size of lisp s-expressions. This version is based on measuring the size of what I call lisp m-expressions, which are lisp…

This is yet another version of the course notes in chao-dyn/9407003. Here we change the universal Turing machine that is used to measure program-size complexity so that the constants in our information-theoretic incompleteness theorems are…

This book is the final version of a course on algorithmic information theory and the epistemology of mathematics and physics. This is camera-ready copy prepared for publication as a book, but at the last minute I decided to publish it…

A remarkable new definition of a self-delimiting universal Turing machine is presented that is easy to program and runs very quickly. This provides a new foundation for algorithmic information theory. This new universal Turing machine is…

The proof of information inequalities and identities under linear constraints on the information measures is an important problem in information theory. For this purpose, ITIP and other variant algorithms have been developed and…

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…

This is a shortened version of "The Limits of Mathematics--Course Outline & Software" (IBM Research Report RC 19324, December 1993) in which all Mathematica code has either been deleted or, if absolutely necessary, replaced by C code. The…

Formally verifying the correctness of mathematical proofs is more accessible than ever, however, the learning curve remains steep for many of the state-of-the-art interactive theorem provers (ITP). Deriving the most appropriate subsequent…

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…

We consider partially-specified optimization problems where the goal is to actively, but efficiently, acquire missing information about the problem in order to solve it. An algorithm designer wishes to solve a linear program (LP), $\max…

The best way to understand complex data structures or algorithm is to see them in action. The present work presents a new tool, especially useful for students and lecturers in computer science. It is written in Java and developed at…

The paper introduces the notion of off-line justification for Answer Set Programming (ASP). Justifications provide a graph-based explanation of the truth value of an atom w.r.t. a given answer set. The paper extends also this notion to…

Information theory plays a central role in establishing fundamental limits on what any learning or estimation algorithm can -- and cannot -- achieve, regardless of computational power. In this chapter, we provide an introduction to these…

We present an information-theoretic framework for understanding overfitting and underfitting in machine learning and prove the formal undecidability of determining whether an arbitrary classification algorithm will overfit a dataset.…

This application for learning APPROXIMATION ALGORITHM has been designed in Java which will make user comfortable in learning the very complex subject "NP-Completeness" and the solution to NP-Complete problem using approximation algorithm.

This paper studies the low-rank matrix completion problem from an information theoretic perspective. The completion problem is rephrased as a communication problem of an (uncoded) low-rank matrix source over an erasure channel. The paper…

Large language models (LLMs) have seen considerable advancements in natural language understanding tasks, yet there remains a gap to bridge before attaining true artificial general intelligence, especially concerning shortcomings in…

This paper contributes to the area of inductive logic programming by presenting a new learning framework that allows the learning of weak constraints in Answer Set Programming (ASP). The framework, called Learning from Ordered Answer Sets,…

This paper establishes a theoretical foundation for understanding the fundamental limits of AI explainability through algorithmic information theory. We formalize explainability as the approximation of complex models by simpler ones,…