45 citations · 158 across the 57 of their papers we have counts for
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Topology Inspired Problems for Cellular Automata, and a Counterexample in Topology
Ville Salo, Ilkka Törmä
We consider two relatively natural topologizations of the set of all cellular automata on a fixed alphabet. The first turns out to be rather pathological, in that the countable spa…
On Derivatives and Subpattern Orders of Countable Subshifts
Ville Salo, Ilkka Törmä
We study the computational and structural aspects of countable two-dimensional SFTs and other subshifts. Our main focus is on the topological derivatives and subpattern posets of t…
A Characterization of Cellular Automata Generated by Idempotents on the Full Shift
Ville Salo
In this article, we discuss the family of cellular automata generated by so-called idempotent cellular automata (CA G such that G^2 = G) on the full shift. We prove a characterizat…
On Nilpotency and Asymptotic Nilpotency of Cellular Automata
Ville Salo
We prove a conjecture of P. Guillon and G. Richard by showing that cellular automata that eventually fix all cells to a fixed symbol 0 are nilpotent on S^Z^d for all d. We also bri…
Geometry and Dynamics of the Besicovitch and Weyl Spaces
Ville Salo, Ilkka Törmä
We study the geometric properties of Cantor subshifts in the Besicovitch space, proving that sofic shifts occupy exactly the homotopy classes of simplicial complexes. In addition,…
On Shift Spaces with Algebraic Structure
Ville Salo, Ilkka Törmä
We investigate subshifts with a general algebraic structure and cellular automata on them, with an emphasis on (order-theoretic) lattices. Our main results concern the characteriza…