Related papers: Nontrivial Turmites are Turing-universal
Non-Hermiticity significantly enriches the concepts of symmetry and topology in physics. Particularly, non-Hermiticity gives rise to the ramified symmetries, where the non-Hermitian Hamiltonian $H$ is transformed to $H^\dagger$. For…
The world runs on communicated sequences of symbols, e.g. numerals. Examining both engineered and natural communications networks reveals an unsuspected order that depends on contact with an unpredictable entity. This order has three roots.…
We introduce and study the writhe of a permutation, a circular variant of the well-known inversion number. This simple permutation statistics has several interpretations, which lead to some interesting properties. For a permutation sampled…
Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical…
Beginning with Turing's seminal work in 1950, artificial intelligence proposes that consciousness can be simulated by a Turing machine. This implies a potential theory of everything where the universe is a simulation on a computer, which…
Robots assisting us in factories or homes must learn to make use of objects as tools to perform tasks, e.g., a tray for carrying objects. We consider the problem of learning commonsense knowledge of when a tool may be useful and how its use…
We survey concepts at the frontier of research connecting artificial, animal and human cognition to computation and information processing---from the Turing test to Searle's Chinese Room argument, from Integrated Information Theory to…
Universality is a key hypothesis in mechanistic interpretability -- that different models learn similar features and circuits when trained on similar tasks. In this work, we study the universality hypothesis by examining how small neural…
The two squares theorem of Fermat is a gem in number theory, with a spectacular one-sentence "proof from the Book". Here is a formalisation of this proof, with an interpretation using windmill patterns. The theory behind involves…
Despite having advanced a reaction-diffusion model of ODE's in his 1952 paper on morphogenesis, reflecting his interest in mathematical biology, Alan Turing has never been considered to have approached a definition of Cellular Automata.…
A variant of Turing machines is introduced where the tape is replaced by a single tree which can be manipulated in a style akin to purely functional programming. This yields two benefits: first, the extra structure on the tape can be…
While it is well known that a Turing machine equipped with the ability to flip a fair coin cannot compute more that a standard Turing machine, we show that this is not true for a biased coin. Indeed, any oracle set $X$ may be coded as a…
We present two abstractions for designing modular state machine replication (SMR) protocols: trees and turtles. A tree captures the set of possible state machine histories, while a turtle represents a subprotocol that tries to find…
Place/Transition Petri nets with inhibitor arcs (PTI nets for short), which are a well-known Turing-complete, distributed model of computation, are equipped with a decidable, behavioral equivalence, called pti-place bisimilarity, that…
The Neural Machine Translation (NMT) model is essentially a joint language model conditioned on both the source sentence and partial translation. Therefore, the NMT model naturally involves the mechanism of the Language Model (LM) that…
Simulations of weighted tree automata (wta) are considered. It is shown how such simulations can be decomposed into simpler functional and dual functional simulations also called forward and backward simulations. In addition, it is shown in…
Linearly bounded Turing machines have been mainly studied as acceptors for context-sensitive languages. We define a natural class of infinite automata representing their observable computational behavior, called linearly bounded graphs.…
Unsupervised neural machine translation (NMT) is a recently proposed approach for machine translation which aims to train the model without using any labeled data. The models proposed for unsupervised NMT often use only one shared encoder…
We investigate the capabilities of transformer models on relational reasoning tasks. In these tasks, models are trained on a set of strings encoding abstract relations, and are then tested out-of-distribution on data that contains symbols…
A deterministic finite (semi)automaton is primitive if its transition monoid (semigroup) acting on the set of states has no non-trivial congruences. It is synchronizing if it contains a constant map (transformation). In analogy to…