We study two deterministic analogues of random walks. The first is the chip-firing game, a single player game played by moving chips around a directed graph, popularised by Björner and Lovász. We find an efficient simulation of boolean circuits and Turing machines using instances of the chip-firing game - after assigning a fixed strategy to the player. The second is the Propp machine, or the rotor router model, a quasirandom model intro- duced by Priezzhev. We improve results of Kijima et al. and show a bound of O(m) on the discrepancy of this process from a random walk on d-regular graphs with m edges. 1
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:448348 |
| Date | January 2021 |
| Creators | Mittal, Parth |
| Contributors | Koucký, Michal, Dvořák, Zdeněk |
| Source Sets | Czech ETDs |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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