Abstract
A self-mapping M: X → X of a nonempty set X has the Period-Two-Property (p2p) if M2x = x holds for every Af-periodic point x ∈ X. Let X be the set of all (0, 1) -labelings x: V →(0, 1) of the set of vertices F of a locally finite connected graph G. For x ∈ X let Mx ∈ X label v e V by the majority bit that x applies to its neighbors, retaining v’s x-label in case of a tie. We show that M has the p2p if there is a finite bound on the degrees in G and 1/n log b→0, where bnis the number of v ∈ V at a distance at most n from a fixed vertex v ∈ V.
Original language | English |
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Pages (from-to) | 1649-1667 |
Number of pages | 19 |
Journal | Transactions of the American Mathematical Society |
Volume | 347 |
Issue number | 5 |
DOIs | |
State | Published - May 1995 |
Keywords
- Cellular automata
- Infinite graphs
- Majority rule
- Period-two
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics