Related papers: Observations on the Halting Problem

This paper discusses experiments with single-particle systems, some of whose states appear to be entangled. It shows that the interpretation of the experiments in terms of entanglement is ill-defined. Three forms of ambiguity are discussed.…

A recent rebuttal to criticism of Bell's analysis is shown to be defective by fault of failure to consider all hypothetical conditions input into the derivation of Bell Inequalitites.

Three notions of random stopping times exist in the literature. We introduce two concepts of equivalence of random stopping times, motivated by optimal stopping problems and stopping games respectively. We prove that these two concepts…

In the paper it is demonstrated that Bells theorem is an unprovable theorem.

In this work we tried to prove the lonely runner conjecture also known as the view obstruction problem.

The traditional theory of Laplace transformation in its currently prevalent form is unsatisfactory. Its deficiencies can be traced back to a mismatch of the definition intervals of the original function and of the inverse L-transform. A new…

There are some points in the reply of Horton et al. [http://stacks.iop.org/JPhysA/35/7963] to my comment [quant-ph/0202140] on their paper [quant-ph/0103114] which I cannot let stand without a response. I provide here some clarification of…

Some problems of testology are discussed.

Inspired by recent work of P.-L. Lions on conditional optimal control, we introduce a problem of optimal stopping under bounded rationality: the objective is the expected payoff at the time of stopping, conditioned on another event. For…

This essay aims to propose construction theory, a new domain of theoretical research on machine construction, and use it to shed light on a fundamental relationship between living and computational systems. Specifically, we argue that…

We discuss a non-intuitive situation concerning percentages.

The authors are not satisfied about the analysis.

The article presents the detailed analysis of the watch paradox. It is shown that it arose because of unjustified, as it turned out, identification of watch readings at the moment of its return with the time read by it.

The Lorentz integral transform method is briefly reviewed. The issue of the inversion of the transform, and in particular its ill-posedness, is addressed. It is pointed out that the mathematical term ill-posed is misleading and merely due…

This paper establishes an equivalence between the halting problem in computability theory and the convergence of power series in mathematical analysis.

We reply to the criticism raised by Ao in his Comment (cond-mat/9801180). Being unable to properly treat the Hall conductivity in a mixed state of superconductors, Ao is looking for possible mistakes in microscopic and phenomenological…

This is the second installment to the project initiated in [Ma3]. In the first Part, I argued that both philosophy and technique of the perturbative renormalization in quantum field theory could be meaningfully transplanted to the theory of…

The paper adresses the problem of reasoning with ambiguities. Semantic representations are presented that leave scope relations between quantifiers and/or other operators unspecified. Truth conditions are provided for these representations…

A review article on perturbation theory

Despite numerous attempts at mitigation since the inception of language models, hallucinations remain a persistent problem even in today's frontier LLMs. Why is this? We review existing definitions of hallucination and fold them into a…