1 citations · 1 across the 6 of their papers we have counts for
9 papers
Multiplication cubes and multiplication automata
Johan Kopra
We extend previously known two-dimensional multiplication tiling systems that simulate multiplication by two natural numbers and in base to higher dimensional multipli…
A natural class of cellular automata containing fractional multiplication automata, Rule 30, and others
Johan Kopra
We define the class of rapidly left expansive cellular automata, which contains fractional multiplication automata, Wolfram's Rule 30, and many others. The definition has been shap…
Sofically presented dynamical systems
Johan Kopra, Ville Salo
Systems obtained by quotienting a subshift of finite type (SFT) by another SFT are called finitely presented in the literature. Analogously, if a sofic shift is quotiented by a sof…
Direct Prime Subshifts and Canonical Covers
Johan Kopra
We present a new sufficient criterion to prove that a non-sofic half-synchronized subshift is direct prime. The criterion is based on conjugacy invariant properties of Fischer grap…
On the Trace Subshifts of Fractional Multiplication Automata
Johan Kopra
We address the dynamics of the cellular automaton (CA) that multiplies by in base (for coprime ) by studying its trace subshift. We present a conjugacy of the tra…
Glider automata on all transitive sofic shifts
Johan Kopra
For any infinite transitive sofic shift we construct a reversible cellular automaton (i.e. an automorphism of the shift ) which breaks any given finite point of the subshift…
Dynamics of cellular automata on beta-shifts and direct topological factorizations
Johan Kopra
We consider the range of possible dynamics of cellular automata (CA) on two-sided beta-shifts . We show that any reversible CA has an almost equicontinuous dire…
On computing the Lyapunov exponents of reversible cellular automata
Johan Kopra
We consider the problem of computing the Lyapunov exponents of reversible cellular automata (CA). We show that the class of reversible CA with right Lyapunov exponent cannot be…
Cellular Automata and Powers of
Jarkko Kari, Johan Kopra
We consider one-dimensional cellular automata which multiply numbers by in base for relatively prime integers and . By studying the structure of traces…