On the Impact of Treewidth in the Computational Complexity of Freezing Dynamics

Goles, Éric; Montealegre, Pedro; Wilson, Martín Ríos; Theyssier, Guillaume

doi:10.1007/978-3-030-80049-9_24

Cited by 3 publications

(2 citation statements)

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“…It is not the case for convergent CA. This can be formulated using communication complexity or classical computational complexity of the prediction problem [77,30,62] (see also [33] which generalizes the result to other G). The prediction problem associated to a CA asks for the state of a cell after a given time starting from a given input, a possible formalization is as follows: given an input pattern u ∈ Q Btr where r is the radius of the considered CA, the problem is to determine the value of cell 0 G after t steps starting from a configuration c ∈ [u] (note that by choice of the domain of u, this does not depend on c).…”

Section: Dimension 1: Complexity Gap Between Bounded Change and Conve...mentioning

confidence: 95%

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Cold dynamics in cellular automata: a tutorial

Theyssier

2022

Nat Comput

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This tutorial is about cellular automata that exhibit cold dynamics. By this we mean zero Kolmogorov-Sinai entropy, stabilization of all orbits, trivial asymptotic dynamics, or similar properties. These are essentially transient and irreversible dynamics, but they capture many examples from the literature, ranging from crystal growth to epidemic propagation and symmetric majority vote. A collection of properties is presented and discussed: nilpotency and asymptotic, generic or mu-variants, unique ergodicity, convergence, bounded-changeness, freezingness. They all correspond to the cold dynamics paradigm at various degrees, and we study their links and differences by key examples and results. Besides dynamical considerations, we also focus on computational aspects: we show how such cold cellular automata can still compute under their dynamical constraints, and what are their computational limitations. The purpose of this tutorial is to illustrate how the richness and complexity of the model of cellular automata are preserved under such strong constraints. By putting forward some open questions, it is also an invitation to look more closely at this cold dynamics territory, which is far from being completely understood.

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Section: Dimension 1: Complexity Gap Between Bounded Change and Conve...mentioning

confidence: 95%

“…Following this approach, many results focused on nilpotency or convergence towards a unique attractor [65,3,27]. More recently, freezing automata networks where also considered [33,31,34].…”

Section: Theorem 17 ([62]mentioning

confidence: 99%