Simplified game of life: Algorithms and complexity

K. Chatterjee, R. Ibsen-Jensen, I.R. Jecker, J. Svoboda, in:, 45th International Symposium on Mathematical Foundations of Computer Science, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020.

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Department
Series Title
LIPIcs
Abstract
Game of Life is a simple and elegant model to study dynamical system over networks. The model consists of a graph where every vertex has one of two types, namely, dead or alive. A configuration is a mapping of the vertices to the types. An update rule describes how the type of a vertex is updated given the types of its neighbors. In every round, all vertices are updated synchronously, which leads to a configuration update. While in general, Game of Life allows a broad range of update rules, we focus on two simple families of update rules, namely, underpopulation and overpopulation, that model several interesting dynamics studied in the literature. In both settings, a dead vertex requires at least a desired number of live neighbors to become alive. For underpopulation (resp., overpopulation), a live vertex requires at least (resp. at most) a desired number of live neighbors to remain alive. We study the basic computation problems, e.g., configuration reachability, for these two families of rules. For underpopulation rules, we show that these problems can be solved in polynomial time, whereas for overpopulation rules they are PSPACE-complete.
Publishing Year
Date Published
2020-08-18
Proceedings Title
45th International Symposium on Mathematical Foundations of Computer Science
Acknowledgement
Krishnendu Chatterjee: The research was partially supported by the Vienna Science and Technology Fund (WWTF) Project ICT15-003. Ismaël Jecker: This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.
Volume
170
Article Number
22:1-22:13
Conference
MFCS: Symposium on Mathematical Foundations of Computer Science
Conference Location
Prague, Czech Republic
Conference Date
2020-08-24 – 2020-08-28
ISSN
IST-REx-ID

Cite this

Chatterjee K, Ibsen-Jensen R, Jecker IR, Svoboda J. Simplified game of life: Algorithms and complexity. In: 45th International Symposium on Mathematical Foundations of Computer Science. Vol 170. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.MFCS.2020.22
Chatterjee, K., Ibsen-Jensen, R., Jecker, I. R., & Svoboda, J. (2020). Simplified game of life: Algorithms and complexity. In 45th International Symposium on Mathematical Foundations of Computer Science (Vol. 170). Prague, Czech Republic: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.MFCS.2020.22
Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, Ismael R Jecker, and Jakub Svoboda. “Simplified Game of Life: Algorithms and Complexity.” In 45th International Symposium on Mathematical Foundations of Computer Science, Vol. 170. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.MFCS.2020.22.
K. Chatterjee, R. Ibsen-Jensen, I. R. Jecker, and J. Svoboda, “Simplified game of life: Algorithms and complexity,” in 45th International Symposium on Mathematical Foundations of Computer Science, Prague, Czech Republic, 2020, vol. 170.
Chatterjee K, Ibsen-Jensen R, Jecker IR, Svoboda J. 2020. Simplified game of life: Algorithms and complexity. 45th International Symposium on Mathematical Foundations of Computer Science. MFCS: Symposium on Mathematical Foundations of Computer Science, LIPIcs, vol. 170.
Chatterjee, Krishnendu, et al. “Simplified Game of Life: Algorithms and Complexity.” 45th International Symposium on Mathematical Foundations of Computer Science, vol. 170, 22:1-22:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.MFCS.2020.22.
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2020-09-21
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