2 citations · 3 across the 5 of their papers we have counts for
6 papers · 1 filter
Cellular Automata vs. Quasisturmian Shifts
Marcus Pivato
If L=Z^D and A is a finite set, then A^L is a compact space. A cellular automaton (CA) is a continuous transformation F:A^L--> A^L that commutes with all shift maps. A quasisturmia…
Invariant measures for bipermutative cellular automata
Marcus Pivato
A `right-sided, nearest neighbour cellular automaton' (RNNCA) is a continuous transformation F:A^Z-->A^Z determined by a local rule f:A^{0,1}-->A so that, for any a in A^Z and any…
Asymptotic Randomization of Sofic Shifts by Linear Cellular Automata
Marcus Pivato, Reem Yassawi
Let M=Z^D be a D-dimensional lattice, and let A be an abelian group. A^M is then a compact abelian group; a `linear cellular automaton' (LCA) is a topological group endomorphism Φ:…
Linear cellular automata, asymptotic randomization, and entropy
Marcus Pivato
If A=Z/2, then A^Z is a compact abelian group. A `linear cellular automaton' is a shift-commuting endomorphism F of A^Z. If P is a probability measure on A^Z, then F `asymptoticall…
Asymptotic behaviour of measures with long range correlations under the action of cellular automata
Marcus Pivato, Reem Yassawi
This paper has been withdrawn by the authors, due an error involving the weak* convergence argument in section 2
Multiplicative Cellular Automata on Nilpotent Groups: Structure, Entropy, and Asymptotics
Marcus Pivato
If M is a monoid (e.g. the lattice Z^D), and G is a finite (nonabelian) group, then G^M is a compact group; a `multiplicative cellular automaton' (MCA) is a continuous transformati…