12 papers · ranked by Valyu relevance
Joel David Hamkins, Theodor Nenu
| 1. | The halting problem | 2 | | --- | --- | --- | | 2. | Did Turing prove the undecidability of the halting problem? | 2 | | 3. | The prima facie case against the Turing attribution | 4 | | 4. | The circle-free problem | 5 | | 5. | The symbol-printing problem | 10 | | 6. | The Entscheidungsproblem | 12 | | 7. |…
Nicholas J. Macias
This paper describes Turing's Halting Problem (HP), and reviews the classic proof that no function exists that can solve HP. The concept of a "Context-Dependent Function" (CDF), whose behavior varies based on seemingly irrelevant changes to a program calling that function, is introduced, and the proof of HP's…
Bill Stoddart
The halting problem is considered to be an essential part of the theoretical background to computing. That halting is not in general computable has been "proved" in many text books and taught on many computer science courses, and is supposed to illustrate the limits of computation. However, Eric Hehner has a dissenting…
Gabriel A. Melo, Marcos R. O. A. Máximo, Nei Y. Soma, Paulo A. L. Castro
'Paulo A. L. Castro'] 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, which is also equivalent to a reduction to Turing’s Halting…
Abhinav Muraleedharan
Can a Turing Machine simulate the human mind? If the Church-Turing thesis is assumed to be true, then a Turing Machine should be able to simulate the human mind. In this paper, I challenge that assumption by providing strong mathematical arguments against the Church-Turing thesis. First, I show that there are decision…
Mark Inman
This article describes a Turing machine which can solve for β 0 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 decides over β 0 implies inconsistency in ZFC. We then discover that unrestricted use of the…
Luís Tarrataca, Andreas Wichert, Gerardo Adesso
Classical models of computation traditionally resort to halting schemes in order to enquire about the state of a computation. In such schemes, a computational process is responsible for signaling an end of a calculation by setting a halt bit, which needs to be systematically checked by an observer. The capacity of…
Hannah Cairns
The abelian sandpile model is a simple combinatorial model for critical behaviour, with the abelian property that the order in which we make moves does not change the final outcome of the game. This might seem to restrict the model's computational ability, but we will show that, given three dimensions to work with, the…
Fernando Soler-Toscano, Hector Zenil, Jean-Paul Delahaye, Nicolas Gauvrit + 1 more
'Nicolas Gauvrit' 'Matthias Dehmer'] Drawing on various notions from theoretical computer science, we present a novel numerical approach, motivated by the notion of algorithmic probability, to the problem of approximating the Kolmogorov-Chaitin complexity of short strings. The method is an alternative to the…
W. Richard Stark
The cellular automata model was described by John von Neumann and his friends in the 1950s as a representation of information processing in multicellular tissue. With crystalline arrays of cells and synchronous activity, it missed the mark (Stark and Hughes, BioSystems 55:107-117, [22]). Recently, amorphous computing…
Shuvendu K. Lahiri, Chao Wang, Bernd Finkbeiner, Christopher Hahn + 2 more
\usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\omega $$\end{document} -regular Hyperproperties Authors: ['Shuvendu K. Lahiri' 'Chao Wang' 'Bernd Finkbeiner'…
Neha Sapkal, Nino Mancini, Divya Sthanu Kumar, Nico Spiller + 9 more
Walking is a complex motor program involving coordinated and distributed activity across the brain and the spinal cord. Halting appropriately at the correct time is a critical but often overlooked component of walking control. While recent studies have delineated specific genetically defined neuronal populations in the…