Related papers: The Complexity of Logarithmic Space Bounded Counti…
Complexity theory provides a wealth of complexity classes for analyzing the complexity of decision and counting problems. Despite the practical relevance of enumeration problems, the tools provided by complexity theory for this important…
We develop the theory of probabilistic variants of the one-category and diagonal topological complexity, which bound the classical LS-category and topological complexity from below. Unlike any other classical or probabilistic invariants,…
This is yet another version of the course notes in chao-dyn/9407003. Here we change the universal Turing machine that is used to measure program-size complexity so that the constants in our information-theoretic incompleteness theorems are…
In the paper we define three new complexity classes for Turing Machine undecidable problems inspired by the famous Cook/Levin's NP-complete complexity class for intractable problems. These are U-complete (Universal complete), D-complete…
Complexity classes such as $\#\mathbf{P}$, $\oplus\mathbf{P}$, $\mathbf{GapP}$, $\mathbf{OptP}$, $\mathbf{NPMV}$, or the class of fuzzy languages realised by polynomial-time fuzzy nondeterministic Turing machines, can all be described in…
Classifying isomorphism classes of group gradings on algebras presents a compelling challenge, particularly within the realms of non-simple and infinite-dimensional algebras, which have been relatively unexplored. This study focuses on a…
This was submitted as a final project for CS254B, taught by Li Yang Tan and Tom Knowles. The field of Circuit Complexity utilises careful analysis of Boolean Circuit Functions in order to extract meaningful information about a range of…
We suggest analyzing neural networks through the prism of space constraints. We observe that most training algorithms applied in practice use bounded memory, which enables us to use a new notion introduced in the study of space-time…
The Skolem Problem asks, given an integer linear recurrence sequence (LRS), to determine whether the sequence contains a zero term or not. Its decidability is a longstanding open problem in theoretical computer science and automata theory.…
A significant progress has been made in the past three decades over the study of combinatorial NP optimization problems and their associated optimization and approximate classes, such as NPO, PO, APX (or APXP), and PTAS. Unfortunately, a…
The notion of effective topological complexity, introduced by B{\l}aszczyk and Kaluba, deals with using group actions in the configuration space in order to reduce the complexity of the motion planning algorithm. In this article we focus on…
The aim of my thesis is to discuss, develop and apply the newest developments of this fascinating theory connected to modern harmonic analysis. In particular, we investigate some strong convergence result of partial sums of Vilenkin-Fourier…
A language is said to be in catalytic logspace if we can test membership using a deterministic logspace machine that has an additional read/write tape filled with arbitrary data whose contents have to be restored to their original value at…
This paper provides a general result on controlling local Rademacher complexities, which captures in an elegant form to relate the complexities with constraint on the expected norm to the corresponding ones with constraint on the empirical…
Continuing the study of complexity theory of Koepke's Ordinal Turing Machines (OTMs) that was started by Rin, L\"owe and the author, we prove the following results: (1) An analogue of Ladner's theorem for OTMs holds: That is, there are…
This paper takes a computational learning theory approach to a problem of linear systems identification. It is assumed that input signals have only a finite number k of frequency components, and systems to be identified have dimension no…
In this note, we provide a unifying framework to investigate the computational complexity of classical spin models and give the full classification on spin models in terms of system dimensions, randomness, external magnetic fields and types…
Class groups of real quadratic fields represent fundamental structures in algebraic number theory with significant computational implications. While Stark's conjecture establishes theoretical connections between special units and class…
We survey results on the topological complexity of classical configuration spaces of distinct ordered points in orientable surfaces and related spaces, including certain orbit configuration spaces and Eilenberg-Mac Lane spaces associated to…
Polynomial--time constant--space quantum Turing machines (QTMs) and logarithmic--space probabilistic Turing machines (PTMs) recognize uncountably many languages with bounded error (Say and Yakary\i lmaz 2014, arXiv:1411.7647). In this…