Related papers: X-Rule's Precursor is also Logically Universal
An elementary cellular automaton with memory is a chain of finite state machines (cells) updating their state simultaneously and by the same rule. Each cell updates its current state depending on current states of its immediate neighbours…
Computing properties of the set of precursors of a given configuration is a common problem underlying many important questions about cellular automata. Unfortunately, such computations quickly become intractable in dimension greater than…
We have designed a machine that becomes increasingly better at behaving in underspecified circumstances, in a goal-directed way, on the job, by modeling itself and its environment as experience accumulates. Based on principles of…
The rule "defeated(X) $\leftarrow$ attacks(Y,X), $\neg$ defeated(Y)" states that an argument is defeated if it is attacked by an argument that is not defeated. The rule "win(X) $\leftarrow$ move(X,Y), $\neg$ win(Y)" states that in a game a…
In inductive learning of a broad concept, an algorithm should be able to distinguish concept examples from exceptions and noisy data. An approach through recursively finding patterns in exceptions turns out to correspond to the problem of…
For any infinite transitive sofic shift $X$ we construct a reversible cellular automaton (i.e. an automorphism of the shift $X$) which breaks any given finite point of the subshift into a finite collection of gliders traveling into opposing…
In this paper we introduce a novel family of decision lists consisting of highly interpretable models which can be learned efficiently in a greedy manner. The defining property is that all rules are oriented in the same direction.…
How might systematic left-right (L/R) asymmetry of the body plan originate in multicellular animals (and plants)? Somehow, the microscopic handedness of biological molecules must be brought up to macroscopic scales. Basic symmetry…
We have proposed two new evolutionary rules on spatio-iterated games that is not mimic evolution of strategies, and mainly discussed the Prisoner's Dilemma game \cite{toyota2} by the two evoutionary rules \cite{toyota3}. In this paper we…
This paper characterizes optimal classification when individuals adjust their behavior in response to the classification rule. We model the interaction between a designer and a population as a Stackelberg game: the designer selects a…
The emergence of complex behaviors in cellular automata is an area that has been widely developed in recent years with the intention to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic…
Cellular automata generate spatially extended, temporally persistent emergent structures from local update rules. No general method derives the mechanisms of that generation from the rule itself; existing tools reconstruct structure from…
Computation models such as circuits describe sequences of computation steps that are carried out one after the other. In other words, algorithm design is traditionally subject to the restriction imposed by a fixed causal order. We address a…
We consider a random walk on a supercritical Galton-Watson tree with leaves, where the transition probabilities of the walk are determined by biases that are randomly assigned to the edges of the tree. The biases are chosen independently on…
Conway's Game of Life is a two-dimensional cellular automaton. As a dynamical system, it is well-known to be computationally universal, i.e.\ capable of simulating an arbitrary Turing machine. We show that in a sense taking a single…
The principle that rational agents should maximize expected utility or choiceworthiness is intuitively plausible in many ordinary cases of decision-making under uncertainty. But it is less plausible in cases of extreme, low-probability risk…
We study the predictability of emergent phenomena in complex systems. Using nearest neighbor, one-dimensional Cellular Automata (CA) as an example, we show how to construct local coarse-grained descriptions of CA in all classes of Wolfram's…
In cellular automata models a glider gun is an oscillating pattern of non-quiescent states that periodically emits traveling localizations (gliders). The glider streams can be combined to construct functionally complete systems of logical…
The generic limit set of a cellular automaton is a topologically dened set of congurations that intends to capture the asymptotic behaviours while avoiding atypical ones. It was dened by Milnor then studied by Djenaoui and Guillon rst, and…
The classical "game of life" (GOL) due to Conway is a famous mathematical game constructed as a two-dimensional cellular automaton in which each cell is either alive or dead. A set of evolutionary rules determines whether a cell dies,…