Related papers: On Function Description
Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This…
How can one recognize coordination languages and technologies? As this report shows, the common approach that contrasts coordination with computation is intellectually unsound: depending on the selected understanding of the word…
The theoretical limits of 'lossy' data compression algorithms are considered. The complexity of an object as seen by a macroscopic observer is the size of the perceptual code which discards all information that can be lost without altering…
We introduce a uniform representation of general objects that captures the regularities with respect to their structure. It allows a representation of a general class of objects including geometric patterns and images in a sparse, modular,…
Implicit computational complexity, which aims at characterizing complexity classes by machine-independent means, has traditionally been based, on the one hand, on programs and deductive formalisms for free algebras, and on the other hand on…
Kawamura and Cook have developed a framework for studying the computability and complexity theoretic problems over "large" topological spaces. This framework has been applied to study the complexity of the differential operator and the…
It is well known that many theorems in recursion theory can be "relativized". This means that they remain true if partial recursive functions are replaced by functions that are partial recursive relative to some fixed oracle set. Uspensky…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
We introduce a notion of Kolmogorov complexity of unitary transformation, which can (roughly) be understood as the least possible amount of information required to fully describe and reconstruct a given finite unitary transformation. In the…
Query complexity measures the amount of information an algorithm needs about a problem to compute a solution. On a quantum computer there are different realizations of a query and we will show that these are not always equivalent. Our…
The essential variables in a finite function $f$ are defined as variables which occur in $f$ and weigh with the values of that function. The number of essential variables is an important measure of complexity for discrete functions. When…
Classical versions of Kolmogorov complexity are incomputable. Nevertheless, in 1975 Solovay showed that there are computable functions $f > K+O(1)$ such that for infinitely many strings $\sigma$, $f(\sigma)=K(\sigma)+O(1)$, where $K$…
Software developers and maintainers need to read and understand source programs and other software artifacts. The increase in size and complexity of software drastically affects several quality attributes, especially understandability and…
Complex machine learning algorithms are used more and more often in critical tasks involving text data, leading to the development of interpretability methods. Among local methods, two families have emerged: those computing importance…
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…
We introduce a machine free mathematical framework to get a natural formalization of some general notions of infinite computation in the context of Kolmogorov complexity. Namely, the classes Max^{X\to D}_{PR} and Max^{X\to D}_{Rec} of…
There is a longstanding debate whether the Kolmogorov-Arnold representation theorem can explain the use of more than one hidden layer in neural networks. The Kolmogorov-Arnold representation decomposes a multivariate function into an…
This work concerns a comparison of SVM kernel methods in text categorization tasks. In particular I define a kernel function that estimates the similarity between two objects computing by their compressed lengths. In fact, compression…
This paper compares different representations (in the sense of computable analysis) of a number of function spaces that are of interest in analysis. In particular subspace representations inherited from a larger function space are compared…
It is an established fact that for many of the interesting problems quantum algorithms based on queries of the standard oracle bring no significant improvement in comparison to known classical algorithms. It is conceivable that there are…