Related papers: A Tale of Two Turing Machines
There is much to learn from what Turing hastily dismissed as Lady Lovelace s objection. Digital computers can indeed surprise us. Just like a piece of art, algorithms can be designed in such a way as to lead us to question our understanding…
The use of language-model-based question-answering systems to aid humans in completing difficult tasks is limited, in part, by the unreliability of the text these systems generate. Using hard multiple-choice reading comprehension questions…
Explainability and comprehensibility of AI are important requirements for intelligent systems deployed in real-world domains. Users want and frequently need to understand how decisions impacting them are made. Similarly it is important to…
For quantum Turing machines we present three elements: Its components, its time evolution operator and its local transition function. The components are related with the components of deterministic Turing machines, the time evolution…
In the first of this pair of papers, it was proven that that no physical computer can correctly carry out all computational tasks that can be posed to it. The generality of this result follows from its use of a novel definition of…
Our interest is in the design of software systems involving a human-expert interacting -- using natural language -- with a large language model (LLM) on data analysis tasks. For complex problems, it is possible that LLMs can harness human…
A central goal of explainable artificial intelligence (XAI) is to improve the trust relationship in human-AI interaction. One assumption underlying research in transparent AI systems is that explanations help to better assess predictions of…
A novel computing model, called \emph{Probe Machine}, is proposed in this paper. Different from Turing Machine, Probe Machine is a fully-parallel computing model in the sense that it can simultaneously process multiple pairs of data, rather…
In this paper, we prove that it is undecidable whether a set of two polycubes can tile $\mathbb{Z}^3$ by translation. The proof involves a new technique that allows us to simulate two disconnected polycubes with two connected polycubes. By…
The development of intelligent machines is one of the biggest unsolved challenges in computer science. In this paper, we propose some fundamental properties these machines should have, focusing in particular on communication and learning.…
There have been many attempts to solve the P versus NP problem. However, with a new proof method, P not equal NP can be proved. A time limit is set for an arbitrary Turing machine and an input word is rejected on a timeout. The time limit…
Some defenders of so-called `artificial intelligence' believe that machines can understand language. In particular, S{\o}gaard has argued in this journal for a thesis of this sort, on the basis of the idea (1) that where there is semantics…
We extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of computability and decidability on the reals. The resulting computability theory leads to a notion of…
We prove that there is no algorithm to tell whether an arbitrarily constructed Quantum Turing Machine has same time steps for different branches of computation. We, hence, can not avoid the notion of halting to be probabilistic in Quantum…
We consider an old question of Slaman and Steel: whether Turing equivalence is an increasing union of Borel equivalence relations none of which contain a uniformly computable infinite sequence. We show this question is deeply connected to…
Incompleteness theorems of Godel, Turing, Chaitin, and Algorithmic Information Theory have profound epistemological implications. Incompleteness limits our ability to ever understand every observable phenomenon in the universe.…
In 1950, Alan Turing proposed an imitation game as the ultimate test of whether a machine was intelligent: could a machine imitate a human so well that its answers to questions indistinguishable from a human. Ever since, creating…
Word translation is a problem in machine translation that seeks to build models that recover word level correspondence between languages. Recent approaches to this problem have shown that word translation models can learned with very small…
In this talk, some aspects of duality symmetries are presented.
One of the main problems encountered so far with recurrent neural networks is that they struggle to retain long-time information dependencies in their recurrent connections. Neural Turing Machines (NTMs) attempt to mitigate this issue by…