Related papers: A Tale of Two Turing Machines
We give small universal Turing machines with state-symbol pairs of (6, 2), (3, 3) and (2, 4). These machines are weakly universal, which means that they have an infinitely repeated word to the left of their input and another to the right.…
Acknowledging that large language models have learned to use language can open doors to breakthrough language science. Achieving these breakthroughs may require abandoning some long-held ideas about how language knowledge is evaluated and…
The architecture of neural Turing machines is differentiable end to end and is trainable with gradient descent methods. Due to their large unfolded depth Neural Turing Machines are hard to train and because of their linear access of…
We present "Human or Not?", an online game inspired by the Turing test, that measures the capability of AI chatbots to mimic humans in dialog, and of humans to tell bots from other humans. Over the course of a month, the game was played by…
Repair, an important resource for resolving trouble in human-human conversation, remains underexplored in human-LLM interaction. In this study, we investigate how LLMs engage in the interactive process of repair in multi-turn dialogues…
The Turing machine (TM) and the Church thesis have formalized the concept of computable number, this allowed to display non-computable numbers. This paper defines the concept of number "approachable" by a TM and shows that some (if not all)…
The quantum world is fascinating. It presents a description of nature that defies our most rooted concepts about what reality is. For example, quantum objects possess \lq\lq spooky\rq\rq\ properties that allow them to be in multiple places…
Can machines truly think? This question and its answer have many implications that depend, in large part, on any number of assumptions underlying how the issue has been addressed or considered previously. A crucial question, and one that is…
Hypercomputation or super-Turing computation is a ``computation'' that transcends the limit imposed by Turing's model of computability. The field still faces some basic questions, technical (can we mathematically and/or physically build a…
We discuss some claims that certain UCOMP devices can perform hypercomputation (compute Turing-uncomputable functions) or perform super-Turing computation (solve NP-complete problems in polynomial time). We discover that all these claims…
An {\omega}-language is a set of infinite words over a finite alphabet X. We consider the class of recursive {\omega}-languages, i.e. the class of {\omega}-languages accepted by Turing machines with a B\"uchi acceptance condition, which is…
Uncertainty is an inherent property of any complex system, especially those that integrate physical parts or operate in real environments. In this paper, we focus on the Digital Twins of adaptive systems, which are particularly complex to…
We envision a machine capable of solving mathematical problems. Dividing the quantitative reasoning system into two parts: thought processes and cognitive processes, we provide probabilistic descriptions of the architecture.
Machine common sense remains a broad, potentially unbounded problem in artificial intelligence (AI). There is a wide range of strategies that can be employed to make progress on this challenge. This article deals with the aspects of…
The paper investigates whether and how AI systems can realize states of uncertainty. By adopting a functionalist and behavioral perspective, it examines how symbolic, connectionist and hybrid architectures make room for uncertainty. The…
We show that a Turing machine with two single-head one-dimensional tapes cannot recognize the set {x2x'| x \in {0,1}^* and x' is a prefix of x} in real time, although it can do so with three tapes, two two-dimensional tapes, or one two-head…
Quantum mechanics, devoid of any additional assumption, does not give any theoretical constraint on the projection basis to be used for the measurement process. It is shown in this paper that it does neither allow any physical means for an…
Despite the remarkable abilities of Large Language Models (LLMs) to answer questions, they often display a considerable level of overconfidence even when the question does not have a definitive answer. To avoid providing hallucinated…
Uncertainty enters into human reasoning and inference in at least two ways. It is reasonable to suppose that there will be roles for these distinct uses of uncertainty also in automated reasoning.
Nobody knows how language works, but many theories abound. Transformers are a class of neural networks that process language automatically with more success than alternatives, both those based on neural computations and those that rely on…