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- Jarkko Kari, Siamak Taati
- 2013

Reversible cellular automata are seen as microscopic physical models, and their states of macroscopic equilibrium are described using invariant probability measures. Characterizing all the invariant measures of a cellular automaton could be challenging. Nevertheless, we establish a connection between the invariance of Gibbs measures (used in statistical… (More)

A 1D Reversible Cellular Automata (RCA) with forward and backward radius-1 2 neighborhoods is called Rectangular. It was previously conjectured that the conservation laws in 1D Rectangular RCA can be described as linear combinations of independent constant-speed flows to the right or to the left. This is indeed the case; so is a similar statement about a… (More)

We study the group-valued and semigroup-valued conservation laws in cellular automata (CA). We provide examples to distinguish between semigroup-valued, group-valued and real-valued conservation laws. We prove that, even in one-dimensional case, it is undecidable if a CA has any non-trivial conservation law of each type. For a fixed range, each CA has a… (More)

The problem of describing the dynamics of a conserved energy in a cellular automaton in terms of local movements of " particles " (quanta of that energy) has attracted some people's attention. The one-dimensional case was already solved by Fuk´s (2000) and Pivato (2002). For the two-dimensional cellular automata, we show that every (context-free)… (More)

- Tucs Dissertations, Siamak Taati, Supervisor, Jarkko Kari, Cristopher Moore, Bruno Durand +2 others
- 2009

Conservation laws in physics are numerical invariants of the dynamics of a system. In cellular automata (CA), a similar concept has already been defined and studied. To each local pattern of cell states a real value is associated , interpreted as the " energy " (or " mass " , or. . .) of that pattern. The overall " energy " of a configuration is simply the… (More)

We discuss a close link between two seemingly different topics studied in the cellular automata literature: additive conservation laws and invariant probability measures. We provide an elementary proof of a simple correspondence between invariant full-support Bernoulli measures and interaction-free conserved quantities in the case of one-dimensional… (More)

Conservation laws in cellular automata (CA) are studied as an abstraction of the conservation laws observed in nature. In addition to the usual real-valued conservation laws we also consider more general group-valued and semigroup-valued conservation laws. The (algebraic) conservation laws in a CA form a hierarchy, based on the range of the interactions… (More)

A conservation law in a cellular automaton is the statement of the invari-ance of a local and additive energy-like quantity. This chapter reviews the basic theory of conservation laws in cellular automata. A general mathematical framework for formulating conservation laws in cellular automata is presented and several characterizations of them are… (More)

The density classification task is to determine which of the symbols appearing in an array has the majority. A cellular automaton solving this task is required to converge to a uniform configuration with the majority symbol at each site. It is not known whether a one-dimensional cellular automaton with binary alphabet can classify all Bernoulli random… (More)