Towards New Parity Rules with Asynchronous Updating Inspired by Fatès's Rule
Abstract
The parity problem in 1D Cellular Automata is a classifier based on a local rule. If the number of ones in a ring of binary cells is odd then the automaton shall converge to all-one (11...11) else to all-zero (00...00). The objective is to find rules that are related to Fatès's Balanced Rule F but use less active neighborhoods (actions). The method is to analyze the effect of each actions and to find a functioning subset of the 12 actions used in rule F. New rules called HA, HB, HC, HF are defined with 10, 6, 4, 8 actions. Rule HC and HF need only three inputs whereas all others need four. The classification time of the rules was determined by averaging over many simulation runs with random initial configurations. It is almost the same for the rules HA and F, and is longer for the rules HB, HC, HF. In addition, the rule HD is defined, which updates three cells in parallel and works faster. In future work, the functioning and performance of the proposed rules should be treated in a more formal way, and related rules (also with different update schemes) could be considered.
Related
- Fates of Exact Finite-N First-Order Transitions: Coherent Suppression versus Spectral-Collapse Termination
- Modeling of jitter correction methods for asynchronous optical sampling
- Asynchronous Terahertz-field sampling with soliton microcombs
- Synchronous and asynchronous Monte Carlo dynamics of mean-field spin glasses with rotationally invariant couplings: what they share and where they differ
- Identification of damage mechanisms in a metal-matrix composite material via digital volume correlation and finite element model updating
BibTeX
@misc{hoffmann2026towards,
title = {{Towards New Parity Rules with Asynchronous Updating Inspired by Fatès's Rule}},
author = {Rolf Hoffmann},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14026},
eprint = {2610.14026},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14026},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Towards New Parity Rules with Asynchronous Updating Inspired by Fatès's Rule
AU - Rolf Hoffmann
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.14026
UR - https://arxiv.org/abs/2610.14026
AB - The parity problem in 1D Cellular Automata is a classifier based on a local rule. If the number of ones in a ring of binary cells is odd then the automaton shall converge to all-one (11...11) else to all-zero (00...00). The objective is to find rules that are related to Fatès's Balanced Rule F but use less active neighborhoods (actions). The method is to analyze the effect of each actions and to find a functioning subset of the 12 actions used in rule F. New rules called HA, HB, HC, HF are defined with 10, 6, 4, 8 actions. Rule HC and HF need only three inputs whereas all others need four. The classification time of the rules was determined by averaging over many simulation runs with random initial configurations. It is almost the same for the rules HA and F, and is longer for the rules HB, HC, HF. In addition, the rule HD is defined, which updates three cells in parallel and works faster. In future work, the functioning and performance of the proposed rules should be treated in a more formal way, and related rules (also with different update schemes) could be considered.
ER -