Related papers: Nontrivial Turmites are Turing-universal
Several abstract machines that operate on symbolic input alphabets have been proposed in the last decade, for example, symbolic automata or lattice automata. Applications of these types of automata include software security analysis and…
Any quantum system with a non-trivial Hamiltonian is able to simulate any other Hamiltonian evolution provided that a sufficiently large group of unitary control operations is available. We show that there exist finite groups with this…
It is well known that the kind of P systems involved in the definition of the P conjecture is able to solve problems in the complexity class $\mathbf{P}$ by leveraging the uniformity condition. Here we show that these systems are indeed…
This paper goes back to Turing (1936) and treats his machine as a cognitive model (W,D,B), where W is an "external world" represented by memory device (the tape divided into squares), and (D,B) is a simple robot that consists of the…
We study finite-state transducers and their power for transforming infinite words. Infinite sequences of symbols are of paramount importance in a wide range of fields, from formal languages to pure mathematics and physics. While finite…
We construct a two-dimensional Turing machine that is physically universal in both the moving tape and moving head model. In particular, it is mixing of all finite orders in both models. We also provide a variant that is physically…
We consider the structures given by repeatedly generalising the definition of finite state automata by symmetry considerations, and constructing analogues of transition monoids at each step. This approach first gives us non-deterministic…
We are surrounded by spatio-temporal patterns resulting from the interaction of the numerous basic units constituting natural or human-made systems. In presence of diffusive-like coupling, Turing theory has been largely applied to explain…
The mapping of topologically nontrivial gauge transformations in noncommutative gauge theory to corresponding commutative ones is investigated via the operator form of the Seiberg-Witten map. The role of the gauge transformation part of the…
The halting problem for Turing machines is decidable on a set of asymptotic probability one. Specifically, there is a set B of Turing machine programs such that (i) B has asymptotic probability one, so that as the number of states n…
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…
The $\textbf{P}$ vs. $\textbf{NP}$ problem is an important problem in contemporary mathematics and theoretical computer science. Many proofs have been proposed to this problem. This paper proposes a theoretic proof for $\textbf{P}$ vs.…
Fixed point iterations are known to generate chaos, for some values in their parameter range. It is an established fact that Turing Machines are fixed point iterations. However, as these Machines operate in integer space, the standard…
This article aims at providing signal machines as small as possible able to perform any computation (in the classical understanding). After presenting signal machines, it is shown how to get universal ones from Turing machines,…
Social norms underlie all human social interactions, yet formalizing and reasoning with them remains a major challenge for AI systems. We present a novel system for taking social rules of thumb (ROTs) in natural language from the Social…
We prove the Extended Church-Turing Thesis: Every effective algorithm can be efficiently simulated by a Turing machine. This is accomplished by emulating an effective algorithm via an abstract state machine, and simulating such an abstract…
In order to control computational complexity, neural machine translation (NMT) systems convert all rare words outside the vocabulary into a single unk symbol. Previous solution (Luong et al., 2015) resorts to use multiple numbered unks to…
We find limits to the Transformer architecture for language modeling and show it has a universal prediction property in an information-theoretic sense. We further analyze performance in non-asymptotic data regimes to understand the role of…
We describe the Turing Machine, list some of its many influences on the theory of computation and complexity of computations, and illustrate its importance.
We show that there exists a universal quantum Turing machine (UQTM) that can simulate every other QTM until the other QTM has halted and then halt itself with probability one. This extends work by Bernstein and Vazirani who have shown that…