Related papers: Algorithmic complexity for psychology: A user-frie…
A method of random search based on Kolmogorov complexity is proposed and applied to two search problems in group theory. The method is provably effective but not practical, so the applications involve heuristic approximations. Perhaps…
TThe problem is to identify a probability associated with a set of natural numbers, given an infinite data sequence of elements from the set. If the given sequence is drawn i.i.d. and the probability mass function involved (the target)…
This work describes the principled design of a theoretical framework leading to fast and accurate algorithmic information measures on finite multisets of finite strings by means of compression. One distinctive feature of our approach is to…
Kolmogorov Complexity constitutes an integral part of computability theory, information theory, and computational complexity theory -- in the discrete setting of bits and Turing machines. Over real numbers, on the other hand, the…
We lay the foundations of a new theory for algorithms and computational complexity by parameterizing the instances of a computational problem as a moduli scheme. Considering the geometry of the scheme associated to 3-SAT, we separate P and…
The need for analysis of toxicity in new drug candidates and the requirement of doing it fast have asked the consideration of scientists towards the use of artificial intelligence tools to examine toxicity levels and to develop models to a…
We estimate the Kolmogorov complexity of melodies in Irish traditional dance music using Lempel-Ziv compression. The "tunes" of the music are presented in so-called "ABC notation" as simply a sequence of letters from an alphabet: We have no…
A complexity-adaptive tree search algorithm is proposed for $\boldsymbol{G}_N$-coset codes that implements maximum-likelihood (ML) decoding by using a successive decoding schedule. The average complexity is close to that of the successive…
Finding the common subsequences of $L$ multiple strings has many applications in the area of bioinformatics, computational linguistics, and information retrieval. A well-known result states that finding a Longest Common Subsequence (LCS)…
We study practical approximations to Kolmogorov prefix complexity (K) using IMP2, a high-level programming language. Our focus is on investigating the interpreter optimality for this language as the reference machine for the Coding Theorem…
This is a review of aspects of the theory of algorithmic information that may contribute to a framework for formulating questions related to complex highly unpredictable systems. We start by contrasting Shannon Entropy and…
Existing methods for complexity estimation are typically developed for entire documents. This limitation in scope makes them inapplicable for shorter pieces of text, such as health assessment tools. These typically consist of lists of…
Background: Developers spend a lot of their time on understanding source code. Static code analysis tools can draw attention to code that is difficult for developers to understand. However, most of the findings are based on non-validated…
Predicting the runtime complexity of a programming code is an arduous task. In fact, even for humans, it requires a subtle analysis and comprehensive knowledge of algorithms to predict time complexity with high fidelity, given any code. As…
The 2-LCPS problem, first introduced by Chowdhury et al. [Fundam. Inform., 129(4):329-340, 2014], asks one to compute (the length of) a longest palindromic common subsequence between two given strings $A$ and $B$. We show that the 2-LCPS…
This paper investigates the number of quantum queries made to solve the problem of reconstructing an unknown string from its substrings in a certain query model. More concretely, the goal of the problem is to identify an unknown string $S$…
Frequent pattern mining is widely used to find ``important'' or ``interesting'' patterns in data. While it is not easy to mathematically define such patterns, maximal frequent patterns are promising candidates, as frequency is a natural…
String diagrams are an increasingly popular algebraic language for the analysis of graphical models of computations across different research fields. Whereas string diagrams have been thoroughly studied as semantic structures, much less…
The aim of this note is to provide some reference facts for LZW---mostly from Thomas and Cover \cite{Cover:2006aa} and provide a reference for some metrics that can be derived from it. LZW is an algorithm to compute a Kolmogorov Complexity…
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…