Related papers: Arithmetic complexity via effective names for rand…
We answer a question of Downey and Kurtz on left-orderable groups by showing that there is a computable left-orderable group which is not classically isomorphic to a computable group with a computable left-order.
Decomposition classes provide a way of partitioning the Lie algebras of an algebraic group into equivalence classes based on the Jordan decomposition. In this paper, we investigate the decomposition classes of the Lie algebras of connected…
A coarse description of a subset A of omega is a subset D of omega such that the symmetric difference of A and D has asymptotic density 0. We study the extent to which noncomputable information can be effectively recovered from all coarse…
In this dissertation we examine the relationships between the several hierarchies, including the complexity, $\mathrm{LUA}$ (Linearly Universal Avoidance), and shift complexity hierarchies, with an eye towards quantitative bounds on growth…
A set C of reals is said to be negligible if there is no probabilistic algorithm which generates a member of C with positive probability. Various classes have been proven to be negligible, for example the Turing upper-cone of a…
The paper surveys recent progress in understanding geometric, topological and combinatorial properties of large simplicial complexes, focusing mainly on ampleness, connectivity and universality. In the first part of the paper we concentrate…
A semi-measure is a generalization of a probability measure obtained by relaxing the additivity requirement to super-additivity. We introduce and study several randomness notions for left-c.e. semi-measures, a natural class of effectively…
A regular realizability (RR) problem is testing nonemptiness of intersection of some fixed language (filter) with given regular language. We study here complexity of RR problems. It appears that for any language L there exists RR problem…
Computing conceptual structures, like formal concept lattices, is in the age of massive data sets a challenging task. There are various approaches to deal with this, e.g., random sampling, parallelization, or attribute extraction. A so far…
New exceptional (i.e. non-repeating) prime number multiplets are given and formulated in terms of arithmetic progressions, along with laws governing them. Accompanying repeating prime number multiplets are pointed out. Prime number…
To enable the study of open sets in computational approaches to mathematics, lots of extra data and structure on these sets is assumed. For both foundational and mathematical reasons, it is then a natural question, and the subject of this…
While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…
We study the complexity of locally checkable labeling (LCL) problems on $\mathbb{Z}^n$ from the point of view of descriptive set theory, computability theory, and factors of i.i.d. Our results separate various complexity classes that were…
We survey classical and recent developments in numerical linear algebra, focusing on two issues: computational complexity, or arithmetic costs, and numerical stability, or performance under roundoff error. We present a brief account of the…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
Unlike Martin-L\"of randomness and Schnorr randomness, computable randomness has not been defined, except for a few ad hoc cases, outside of Cantor space. This paper offers such a definition (actually, several equivalent definitions), and…
Constructor rewriting systems are said to be cons-free if, roughly, constructor terms in the right-hand sides of rules are subterms of the left-hand sides; the computational intuition is that rules cannot build new data structures. In…
This paper considers the task of learning users' preferences on a combinatorial set of alternatives, as generally used by online configurators, for example. In many settings, only a set of selected alternatives during past interactions is…
We consider a randomised version of Kleene's realisability interpretation of intuitionistic arithmetic in which computability is replaced with randomised computability with positive probability. In particular, we show that (i) the set of…
Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…