Related papers: 27 Open Problems in Kolmogorov Complexity
In this note we briefly survey and propose some open problems related to isoparametric theory.
In this paper we give a definition for quantum Kolmogorov complexity. In the classical setting, the Kolmogorov complexity of a string is the length of the shortest program that can produce this string as its output. It is a measure of the…
A two-dimensional Kolmogorov system with two parameters and having a degenerate condition is studied in this work. We obtain local analytical properties of the system when the parameters vary in a sufficiently small neighborhood of the…
Due to M\"{u}ller'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 compress classical information. The quantitative amount…
Deformation theory of complex manifolds is a classical subject with recent new advances in the noncompact case using both algebraic and analytic methods. In this note, we recall some concepts of the existing theory and introduce new notions…
The Kolmogorov complexity of a string is the length of its shortest description. We define a second quantised Kolmogorov complexity where the length of a description is defined to be the average length of its superposition. We discuss this…
This work presents a study of Kolmogorov complexity for general quantum states from the perspective of deterministic-control quantum Turing Machines (dcq-TM). We extend the dcq-TM model to incorporate mixed state inputs and outputs, and…
The clustering objects has become one of themes in many studies, and do not few researchers use the similarity to cluster the instances automatically. However, few research consider using Kommogorov Complexity to get information about…
We develop a theory of classical complexity. We study the relations between classical complexity and entropy, and conjecture that in an isolated system, classical absolute complexity always tends to grow, until it reaches its maximum. We…
We prove the formula C(a,b) = K(a|C(a,b)) + C(b|a,C(a,b)) + O(1) that expresses the plain complexity of a pair in terms of prefix and plain conditional complexities of its components.
We present a treasure trove of open problems in matrix and operator inequalities, of a functional analytic nature, and with various degrees of hardness.
Numerous definitions for complexity have been proposed over the last half century, with little consensus achieved on how to use the term. A definition of complexity is supplied here that is closely related to the Kolmogorov Complexity and…
In [She82], it is shown that four basic functional properties are enough to characterize plain Kolmogorov complexity, hence obtaining an axiomatic characterization of this notion. In this paper, we try to extend this work, both by looking…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
We reconsider some classical natural semantics of integers (namely iterators of functions, cardinals of sets, index of equivalence relations), in the perspective of Kolmogorov complexity. To each such semantics one can attach a simple…
We give a summary of known results on Matveev's complexity of compact 3-manifolds. The only relevant new result is the classification of all closed orientable irreducible 3-manifolds of complexity 10.
This paper collects some problems that I have encountered during the years, have puzzled me and which, to the best of my knowledge, are still open. Most of them are well-known and have been first stated by other authors. In this sad season…
Loveland complexity is a variant of Kolmogorov complexity, where it is asked to output separately the bits of the desired string, instead of the string itself. Similarly to the resource-bounded Kolmogorov sets we define Loveland sets. We…
This note describes some open problems that can be examined with the purpose of gaining additional insight of how to solve the problem of finding a general classification of geodetic graphs
In connection to the development of the field of Combinatorics on Words, we present a list of open problems and conjectures that were stated during the ten last meetings WORDS. We wish to continually update the present document by adding…