Related papers: Recursion-Theoretic Ranking and Compression
This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the category-theoretic version of the classical area of algebraic semantics. 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…
Sequence representations supporting not only direct access to their symbols, but also rank/select operations, are a fundamental building block in many compressed data structures. Several recent applications need to represent highly…
Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…
The notion of computability closure has been introduced for proving the termination of the combination of higher-order rewriting and beta-reduction. It is also used for strengthening the higher-order recursive path ordering. In the present…
We construct recursion categories from categories of coalgebras. Let $F$ be a nontrivial endofunctor on the category of sets that weakly preserves pullbacks and such that the category $\textbf{Set}_F$ of $F$-coalgebras is complete. The…
Compression of integer sets and sequences has been extensively studied for settings where elements follow a uniform probability distribution. In addition, methods exist that exploit clustering of elements in order to achieve higher…
Recursive coalgebras provide an elegant categorical tool for modelling recursive algorithms and analysing their termination and correctness. By considering coalgebras over categories of suitably indexed families, the correctness of the…
This work is motivated by the problem of finding the limit of the applicability of the first incompleteness theorem ($\sf G1$). A natural question is: can we find a minimal theory for which $\sf G1$ holds? We examine the Turing degree…
A fully tensorial theoretical framework for hypercomplex-valued neural networks is presented. The proposed approach enables neural network architectures to operate on data defined over arbitrary finite-dimensional algebras. The central…
By the sometimes so-called MAIN THEOREM of Recursive Analysis, every computable real function is necessarily continuous. Weihrauch and Zheng (TCS'2000), Brattka (MLQ'2005), and Ziegler (ToCS'2006) have considered different relaxed notions…
A relatively new topic in computability theory is the study of notions of computation that are robust against mistakes on some kind of small set. However, despite the recent popularity of this topic relatively foundational questions about…
A set is introreducible if it can be computed by every infinite subset of itself. Such a set can be thought of as coding information very robustly. We investigate introreducible sets and related notions. Our two main results are that the…
We study the problem of enumerating answers of Conjunctive Queries ranked according to a given ranking function. Our main contribution is a novel algorithm with small preprocessing time, logarithmic delay, and non-trivial space usage during…
We investigate the existence of a class of ZFC-provably total recursive unary functions, given certain constraints, and apply some of those results to show that, for $\Sigma_1$-sound set theory, ZFC$\not\vdash P<NP$.
We introduce and characterize a particularly tractable class of unital type 1 C*-algebras with bounded dimension of irreducible representations. Algebras in this class are called recursive subhomogeneous algebras, and they have an inductive…
Contemporary natural language processing (NLP) revolves around learning from latent document representations, generated either implicitly by neural language models or explicitly by methods such as doc2vec or similar. One of the key…
This paper establishes new restricted isometry conditions for compressed sensing and affine rank minimization. It is shown for compressed sensing that $\delta_{k}^A+\theta_{k,k}^A < 1$ guarantees the exact recovery of all $k$ sparse signals…
Deep neural networks have achieved state-of-the-art performance across numerous applications, but their high memory and computational demands present significant challenges, particularly in resource-constrained environments. Model…
Additive CA on a cylinder of size $n$ can be represented by 01-string $V$ of length $n$ which is its rule. We study a problem: a class $S$ of rules given, for any $V\in S$ describe all sizes $n', n'>n,$ of cylinders such that extension of…