Related papers: Observations on the Halting Problem
The halting problem is considered to be an essential part of the theoretical background to computing. That halting is not in general computable has supposedly been proved in many text books and taught on many computer science courses, in…
The problem of time, considered as a problem in the usual physical context, is reflected in relation with the paper by Kauffman and Smolin (gr-qc/9703026). It is shown that the problem is a misposed problem in the sense that it was raised…
A consistently specified halting function may be computed.
Although the halting problem is undecidable, imperfect testers that fail on some instances are possible. Such instances are called hard for the tester. One variant of imperfect testers replies "I don't know" on hard instances, another…
The Halting Problem is a version of the Liar's Paradox.
It is shown that the halting problem cannot be solved consistently in both the Schrodinger and Heisenberg pictures of quantum dynamics. The existence of the halting machine, which is assumed from quantum theory, leads into a contradiction…
I argue that the Hole Argument is based on a misleading use of the mathematical formalism of general relativity. If one is attentive to mathematical practice, I will argue, the Hole Argument is blocked.
Attempts to quantize light in a manifestly Lorentz covariant manner fail because of the indefinite metric problem. Here an error in the interpretation is uncovered that is at the root of this problem.
We position Turing's result regarding the undecidability of the halting problem as a result about programs rather than machines. The mere requirement that a program of a certain kind must solve the halting problem for all programs of that…
The halting problem is undecidable --- but can it be solved for "most" inputs? This natural question was considered in a number of papers, in different settings. We revisit their results and show that most of them can be easily proven in a…
The interpretation of an experimental realization of Wheeler's delayed-choice gedanken experiment is discussed and called into question.
We find it absurd that Walliser [1] essentially used the same analysis and obtained identical results as reported in [3], yet arrived at different conclusions. Namely, based on an incomplete theory and using erroneous arguments, he not only…
A shortcoming in the authors' interpretation of this beautiful new experiment is pointed out and briefly discussed.
Understanding the transition to turbulence has been impeded by a modeling oversight
A critical note on some of the existing proposals for performing the "delayed choice" experiment is placed. By abandoning the original idea and intention, some modern theoretical proposals and experimental evidence are simply incorrectly…
The inner alignment problem, which asserts whether an arbitrary artificial intelligence (AI) model satisfices a non-trivial alignment function of its outputs given its inputs, is undecidable. This is rigorously proved by Rice's theorem,…
The purpose of this paper is to address some criticisms recently raised by John Horty in two articles against the validity of two commonly accepted defeasible reasoning patterns, viz. reinstatement and floating conclusions. I shall argue…
There is a serious mistake in the proof.
Since many real-world problems arising in the fields of compiler optimisation, automated software engineering, formal proof systems, and so forth are equivalent to the Halting Problem--the most notorious undecidable problem--there is a…
We consider retarded settings in the context of a Bell-type experiment. The retarded setting is defined as the value the setting would have taken were it not for some external intervention (for example, by a human). We derive retarded Bell…