We prove nonhalting of the Turing machine dubbed "Skelet #17", known to be one of the toughest 5-state, 2-symbol Turing machines to analyze. Combined with the efforts of The Busy Beaver Challenge, we are therefore able to show that BB(5), the fifth B...
We want in this article to show the usefulness of Quantum Turing Machine (QTM) in a high-level didactic context as well as in theoretical studies. We use QTM to show its equivalence with quantum circuit model for Deutsch and Deutsch-Jozsa algorithms....
Infinite time Turing machines are extended in several ways to allow for iterated oracle calls. The expressive power of these machines is discussed and in some cases determined....
This is a typeset version of Alan Turing's Second World War research paper \textit{The Applications of Probability to Cryptography}. A companion paper \textit{Paper on Statistics of Repetitions} is also available in typeset form from arXiv at arXiv:1...
This game serves as a social Turing test for the modern era. It highlights the thin line between human-like responses and actual human logic. Since AI now uses advanced tools to mimic us, â¦
Here's the deal: You're in this digital guessing game, trying to figure out if you're texting with a human or an AI that's learned to use emojis like a pro. "Human or Not" takes the classic Turing â¦
Computer science has grown rapidly since its inception in the 1950s and the pioneers in the field are celebrated annually by the A.M. Turing Award. In this paper, we attempt to shed light on the path to influential computer scientists by examining th...
Extending results of Schindler [math.LO/0106087] and Hamkins and Welch [math.LO/0212046], we establish in the context of infinite time Turing machines that P is properly contained in NP intersect coNP. Furthermore, NP intersect coNP is exactly the...
The Church-Turing Thesis confuses numerical computations with symbolic computations. In particular, any model of computability in which equality is not definable, such as the lambda-models underpinning higher-order programming languages, is not equiv...