相关论文: Post's problem for supertasks has both positive an…
Beginning with Turing's seminal work in 1950, artificial intelligence proposes that consciousness can be simulated by a Turing machine. This implies a potential theory of everything where the universe is a simulation on a computer, which…
In this paper we are interested in computability aspects of subshifts and in particular Turing degrees of 2-dimensional SFTs (i.e. tilings). To be more precise, we prove that given any \pizu subset $P$ of $\{0,1\}^\NN$ there is a SFT $X$…
We consider the uniform parallel machines scheduling problem in the context of optimistic bilevel optimization, where two speed options are considered. In this scenario, the leader aims to minimize the weighted number of tardy jobs, while…
This article describes a Turing machine which can solve for $\beta^{'}$ which is RE-complete. RE-complete problems are proven to be undecidable by Turing's accepted proof on the Entscheidungsproblem. Thus, constructing a machine which…
This paper is devoted to the study of the existence of positive solutions for a problem related to a higher order fractional differential equation involving a nonlinear term depending on a fractional differential operator,…
I present a novel mathematical technique for dealing with the infinities arising from divergent sums and integrals. It assigns them fine-grained infinite values from the set of hyperreal numbers in a manner that refines the standard…
We consider the following problem for various infinite time machines. If a real is computable relative to large set of oracles such as a set of full measure or just of positive measure, a comeager set, or a nonmeager Borel set, is it…
We consider the impact of ambiguity on the optimal timing of a class of two-dimensional integral option contracts when the exercise payoff is a positively homogeneous measurable function. Hence, the considered class of exercise payoffs…
We establish a positivity property for a class of semilinear elliptic problems involving indefinite sublinear nonlinearities. Namely, we show that any nontrivial nonnegative solution is positive for a class of problems the strong maximum…
We prove that endowing a real-time probabilistic or quantum computer with the ability of postselection increases its computational power. For this purpose, we provide a new model of finite automata with postselection, and compare it with…
We develop a general theory of jump operators, which is intended to provide an abstraction of the notion of "limit-computability" on represented spaces. Jump operators also provide a framework with a strong categorical flavor for…
In this work, we introduce an interior-point method that employs tensor decompositions to efficiently represent and manipulate the variables and constraints of semidefinite programs, targeting problems where the solutions may not be…
This paper contains selected applications of the new tangential extremal principles and related results developed in Part I to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite…
We state a version of the P=?NP problem for infinite time Turing machines. It is observed that P not= NP for this version.
We introduce a notion of real-valued reward testing for probabilistic processes by extending the traditional nonnegative-reward testing with negative rewards. In this richer testing framework, the may and must preorders turn out to be…
As an inverse problem, we recover the topology of the effective spacetime that a system lies in, in an operational way. This means that from a series of experiments we get a set of points corresponding to events. This continues the previous…
Deterministic synchronous systems consisting of two finite automata running in opposite directions on a shared read-only input are studied with respect to their ability to perform reversible computations, which means that the automata are…
It is considered a semilinear elliptic partial differential equation in $\mathbb{R}^N$ with a potential that may vanish at infinity and a nonlinear term with subcritical growth. A positive solution is proved to exist depending on the…
There is a way of assigning a realizability notion to each degree of incomputability. In our setting, we make use of Weihrauch degrees (degrees of incomputability/discontinuity of partial multi-valued functions) to obtain Lifschitz-like…
We establish critical and subcritical sharp Trudinger-Moser inequalities for fractional dimensions on the whole space. Moreover, we obtain asymptotic lower and upper bounds for the fractional subcritical Trudinger-Moser supremum from which…