Related papers: Probabilistic cellular automata with Andrei Toom
The donation game is a well-established framework for studying the emergence and evolution of cooperation in multi-agent systems. The cooperative behavior can be influenced by the environmental noise in partially observable settings and by…
We study the notion of limit sets of cellular automata associated with probability measures (mu-limit sets). This notion was introduced by P. Kurka and A. Maass. It is a refinement of the classical notion of omega-limit sets dealing with…
A cellular automaton is a parallel synchronous computing model, which consists in a juxtaposition of finite automata whose state evolves according to that of their neighbors. It induces a dynamical system on the set of configurations, i.e.…
We prove that endowing a real-time probabilistic or quantum computer with the ability of postselection increases its computational power. For this purpose, we provide a new model of finite automata with postselection, and compare it with…
Starting from integrable cellular automata we present a novel form of Painlev\'e equations. These equations are discrete in both the independent variable and the dependent one. We show that they capture the essence of the behavior of the…
Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant…
Studies of quantum computer implementations suggest cellular quantum computer architectures. These architectures can simulate the evolution of quantum cellular automata, which can possibly simulate both quantum and classical physical…
We show that quantum cellular automata naturally form the degree-zero part of a coarse homology theory. The recent result of Ji and Yang that the space of QCA forms an Omega-spectrum in the sense of algebraic topology is a direct…
Artificial intelligence commonly refers to the science and engineering of artificial systems that can carry out tasks generally associated with requiring aspects of human intelligence, such as playing games, translating languages, and…
This paper is the continuation of our earlier considerations on cellular automata with Toom local rule (TCA) as the alternative to kinetic Ising systems. The arguments for TCA stationary states not being the equilibrium states are found in…
This report documents the work of our group (named SymBa) at the ALICE 2026 workshop in Copenhagen. Inspired by the pioneering work by Nils Aall Barricelli on symbiogenesis of numerical organisms (i.e., 1D cellular automata) in 1953 (70+…
Cellular automata are both computational and dynamical systems. We give a complete classification of the dynamic behaviour of elementary cellular automata (ECA) in terms of fundamental dynamic system notions such as sensitivity and…
Probabilistic automata (PAs) have been successfully applied in formal verification of concurrent and stochastic systems. Efficient model checking algorithms have been studied, where the most often used logics for expressing properties are…
Wolfram has provided a qualitative classification of cellular automata(CA) rules according to which, there exits a class of CA rules (called Class 4) which exhibit complex pattern formation and long-lived dynamical activity (long…
The year of 2024 marks the 25th anniversary of the publication of evoloops, an evolutionary variant of Chris Langton's self-reproducing loops which proved constructively that Darwinian evolution of self-reproducing organisms by variation…
From the perspective of the large deviations theory of occupational measures, the paper considers Probabilistic Cellular Automata (PCA) as Markov chains on infinite dimensional space. It turns out that for a wide range of PCA, the…
We investigate one-dimensional elementary probabilistic cellular automata (PCA) whose dynamics in first-order mean-field approximation yields discrete logisticlike growth models for a single-species unstructured population with…
We construct a cellular automaton (CA) model that describes the movement of a particle in a disordered system. The mathematical properties of the CA model were examined by varying the configuration of grid and determining the number of…
In this paper we consider cellular automata $(\mathfrak{G},\Phi)$ with algebraic local rules and such that $\mathfrak{G}$ is a topological Markov chain which has a structure compatible to this local rule. We characterize such cellular…
This paper presents an application of the Infinite Unit Axiom, introduced by Yaroslav Sergeyev, (see [11] - [14]) to the development of one-dimensional cellular automata. This application allows the establishment of a new and more precise…