Kuchar, Cyril (2026) Decentralized Diagnosis Method with Probabilistic Cellular Automata. Bachelor's Thesis, Applied Mathematics.
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Abstract
This thesis explores how decentralized networks can detect failures using only local information. We study three different probabilistic cellular automata models on a two-dimensional grid where each cell is either neutral, alert or defective. The goal is straightforward: if too many defects are present, alerts should spread everywhere, otherwise, they should stay localized. The first model, QuorumD, spreads alerts in all directions and is investigated through simulations. These reveal clear critical points where the system switches from coexistence to full invasion. The second and third models have a preferred direction of propagation, making them easier to analyze mathematically. For these directional models, we prove that phase transitions occur for three different initial setups: starting with a single alert, a single defect and an initial density of defects. Together, these results show that local probabilistic rules can reliably signal when a system has crossed a critical failure threshold, suggesting a promising path toward decentralized diagnosis.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Szabo, R. and Donderwinkel, S.A. |
| Degree programme: | Applied Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 03 Jul 2026 13:42 |
| Last Modified: | 03 Jul 2026 13:42 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37331 |
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