Related papers: Computational Complexity of Space-Bounded Real Num…
For each positive integer k, we describe a map f from the complex plane to a suitable non-complete complex locally convex space such that f is k times continuously complex differentiable but not k+1 times, and hence not complex analytic. We…
Space complexity is a key field of study in theoretical computer science. In the quantum setting there are clear motivations to understand the power of space-restricted computation, as qubits are an especially precious and limited resource.…
Constraint propagation is one of the techniques central to the success of constraint programming. To reduce search, fast algorithms associated with each constraint prune the domains of variables. With global (or non-binary) constraints, the…
A real number is called left-computable if there exists a computable increasing sequence of rational numbers converging to it. In this article we are investigating a proper subset of the left-computable numbers. We say that a real number…
A rational number can be naturally presented by an arithmetic computation (AC): a sequence of elementary arithmetic operations starting from a fixed constant, say 1. The asymptotic complexity issues of such a representation are studied e.g.…
This manuscript explores novel complexity results for the feasibility problem over $p$-order cones, extending the foundational work of Porkolab and Khachiyan. By leveraging the intrinsic structure of $p$-order cones, we derive refined…
We give a number of formal proofs of theorems from the field of computable analysis. Many of our results specify executable algorithms that work on infinite inputs by means of operating on finite approximations and are proven correct in the…
The difficulty of explaining non-local correlations in a fixed causal structure sheds new light on the old debate on whether space and time are to be seen as fundamental. Refraining from assuming space-time as given a priori has a number of…
In [8] the authors initiate the study of selective versions of the notion of $\theta$-separability in non-regular spaces. In this paper we continue this investigation by establishing connections between the familiar cardinal numbers arising…
We will find a lower bound on the recognition complexity of the theories that are nontrivial relative to some equivalence relation (this relation may be equality), namely, each of these theories is consistent with the formula, whose sense…
Let $X$ be a real algebraic variety with set of complex points $X_{\mathbb C}$ and set of real points $X_{\mathbb R}$. A complex slice of $X$ is a transverse intersection of $X_{\mathbb R}$ with a complex subvariety $V$ of $X_{\mathbb C}$.…
In this paper, we determine the complexity of the satisfiability problem for various logics obtained by adding numerical quantifiers, and other constructions, to the traditional syllogistic. In addition, we demonstrate the incompleteness of…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…
There are numerous cases of discrepancies between results obtained in the setting of real Banach spaces and those obtained in the complex context. This article is a modern exposition of the subtle differences between key results and…
The complexity of a computational problem is traditionally quantified based on the hardness of its worst case. This approach has many advantages and has led to a deep and beautiful theory. However, from the practical perspective, this…
We study an infinite system of ordinary differential equations that models the evolution of coagulating and fragmenting clusters, which we assume to be composed of identical units. Under very mild assumptions on the coefficients we prove…
There is a cognitive limit in Human Mind. This cognitive limit has played a decisive role in almost all fields including computer sciences. The cognitive limit replicated in computer sciences is responsible for inherent Computational…
The computational complexity of polynomial ideals and Gr\"obner bases has been studied since the 1980s. In recent years, the related notions of polynomial subalgebras and SAGBI bases have gained more and more attention in computational…
We study the question of what is computable by Turing machines equipped with time travel into the past; i.e., with Deutschian closed timelike curves (CTCs) having no bound on their width or length. An alternative viewpoint is that we study…
We investigate the correspondence between the time and space recognition complexity of languages. For this purpose, we will code the long-continued computations of deterministic two-tape Turing machines by the relatively short-length…