Related papers: Nontrivial Turmites are Turing-universal
Universality in cellular automata theory is a central problem studied and developed from their origins by John von Neumann. In this paper, we present an algorithm where any Turing machine can be converted to one-dimensional cellular…
This paper introduces a new computing model based on the cooperation among Turing machines called orchestrated machines. Like universal Turing machines, orchestrated machines are also designed to simulate Turing machines but they can also…
Chain-of-Thought (CoT) has been shown to empirically improve Transformers' performance, and theoretically increase their expressivity to Turing completeness. However, whether Transformers can learn to generalize to CoT traces longer than…
Turing machines and spin models share a notion of universality according to which some simulate all others. Is there a theory of universality that captures this notion? We set up a categorical framework for universality which includes as…
This paper introduces THUMT, an open-source toolkit for neural machine translation (NMT) developed by the Natural Language Processing Group at Tsinghua University. THUMT implements the standard attention-based encoder-decoder framework on…
We prove that any Turing machine running on inputs of arbitrary length can be simulated by a constant bit-size transformer, as long as the context window is sufficiently long. This improves previous works, which require scaling up either…
Letter-to-letter transducers are a standard formalism for modeling reactive systems. Often, two transducers that model similar systems differ locally from one another, by behaving similarly, up to permutations of the input and output…
For any fixed $k$, a remarkably simple single-tape Turing machine can simulate $k$ independent counters in real time. Informally, a counter is a storage unit that maintains a single integer (initially 0), incrementing it, decrementing it,…
The busy beaver is a well-known specific example of a non-computable function. Whilst many aspect of this problem have been investigated, it is not always easy to find thorough and convincing evidence for the claims made about the…
We describe various computational models based initially, but not exclusively, on that of the Turing machine, that are generalized to allow for transfinitely many computational steps. Variants of such machines are considered that have…
The abstract notion of a Universal Turing machine cannot exist as a physical subsystem without the introduction of noise from an external energy source. Like all other physical systems, physical Turing machines must convert energy sourced…
Machine translation (MT) is a technique that leverages computers to translate human languages automatically. Nowadays, neural machine translation (NMT) which models direct mapping between source and target languages with deep neural…
So far, following the works of A.M. Turing, the algorithms were considered as the mathematical abstraction from which we could write programs for computers whose principle was based on the theoretical concept of Turing machine. We start…
Let $\Omega=\{1,2,...,n\}$ where $n \ge 2$. The {\em shape} of an ordered set partition $P=(P_1,..., P_k)$ of $\Omega$ is the integer partition $\lambda=(\lambda_1,...,\lambda_k)$ defined by $\lambda_i = |P_i|$. Let G be a group of…
We introduce the zeta number, natural halting probability and natural complexity of a Turing machine and we relate them to Chaitin's Omega number, halting probability, and program-size complexity. A classification of Turing machines…
The paper tackles four basic questions associated with human brain as a learning system. How can the brain learn to (1) mentally simulate different external memory aids, (2) perform, in principle, any mental computations using imaginary…
The halting probability of a Turing machine,also known as Chaitin's Omega, is an algorithmically random number with many interesting properties. Since Chaitin's seminal work, many popular expositions have appeared, mainly focusing on the…
Efforts at understanding the computational processes in the brain have met with limited success, despite their importance and potential uses in building intelligent machines. We propose a simple new model which draws on recent findings in…
We explore the relationship between Turing completeness and topological entropy of dynamical systems. We first prove that a natural class of Turing machines that we call "branching Turing machines" (which includes most of the known examples…
We extend the capabilities of neural networks by coupling them to external memory resources, which they can interact with by attentional processes. The combined system is analogous to a Turing Machine or Von Neumann architecture but is…