Related papers: Observations on the Halting Problem
This paper initially aimed at proposing a proof that quasi-dense logics have f.m.p, but it contains a major flaw, unfixable.
In this preliminary note, we will illustrate our ideas on automated mechanisms for termination and non-termination reasoning.
This is an update of my problem list.
We separate the criticisms of Hodges \cite{Hodges2005} and others into those against the algorithm itself and those against its physical implementation. We then point out that {\em all} those against the algorithm are either misleading or…
We discuss some problems with the indefinite integral notation and the way of teaching of integrals in Calculus. Based on the discussion, and in order to avoid mistakes, we propose another notation for indefinite integrals.
We reconsider some important foundational problems of quantum mechanics. After reviewing the measurement problem and discussing its unavoidability, we analyze some proposals to overcome it. This analysis leads us to reconsider the current…
This paper collects some problems that I have encountered during the years, have puzzled me and which, to the best of my knowledge, are still open. Most of them are well-known and have been first stated by other authors. In this sad season…
For a long time, Collatz Conjecture has been assumed to be true, although a formal proof has eluded all efforts to date. In this article, evidence is presented that suggests such an assumption is incorrect. By analysing the stopping times…
The Turing machine halting problem can be explained by several factors, including arithmetic logic irreversibility and memory erasure, which contribute to computational uncertainty due to information loss during computation. Essentially,…
There are several versions of Bell's inequalities, proved in different contexts, using different sets of assumptions. The discussions of their experimental violation often disregard some required assumptions and use loose formulations of…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
The paper deals with a problem of control of a system characterized by the fact that the influence of controls on the dynamics of certain functions of state variables (called observables) is relatively weak and the rates of change of these…
The extended Hamilton's Principle and other methods proposed to handle non-holonomic constraints are considered. They dont agree with each other. By looking at its consistency with D'Alembert's principle for linear non-holonomic…
In this essay, I argue that explicit ethical machines, whose moral principles are inferred through a bottom-up approach, are unable to replicate human-like moral reasoning and cannot be considered moral agents. By utilizing Alan Turing's…
This article demonstrates that the recent proof of the invariant subspace problem, as presented by Khalil et al., is incorrect.
We develop a mathematical theory of entropic regularisation of unbalanced optimal transport problems. Focusing on static formulation and relying on the formalism developed for the unregularised case, we show that unbalanced optimal…
In this paper, we study the ill-posdness of the Cauchy problem for semilinear wave equation with very low regularity, where the nonlinear term depends on $u$ and $\partial_t u$. We prove a ill-posedness result for the "defocusing" case, and…
This paper studies sequential information acquisition by an ambiguity-averse decision maker (DM), who decides how long to collect information before taking an irreversible action. The agent optimizes against the worst-case belief and…
Bell's theorem admits several interpretations or 'solutions', the standard interpretation being 'indeterminism', a next one 'nonlocality'. In this article two further solutions are investigated, termed here 'superdeterminism' and…
We give a definition for Obstacle Problems with measure data and general obstacles. For such problems we prove existence and uniqueness of solutions and consistency with the classical theory of Variational Inequalities. Continuous…