Abstract
General purpose computation on graphics processing units (GPGPU) is a recent trend in areas which heavily depend on linear algebra, in particular solving large systems of linear equations. Many games, both qualitative (e.g. parity games) and quantitative (e.g. mean-payoff games) can be seen as systems of linear equations, too, albeit on more general algebraic structures. Building up on our GPU-based implementation of several solvers for parity games [8], we present in this paper a solver for mean-payoff games. Our implementation uses OpenCL which allows us to execute it without any changes on both the CPU and on the GPU allowing for direct comparison.
We evaluate our implementation on several benchmarks (obtained via reduction from parity games and optimization of controllers for hybrid systems [10]) where we obtain a speedup of up to 10 on the GPU in cases of MPGs with \(20\cdot 10^6\) nodes and \(60\cdot 10^6\) edges.
This work was partially funded and supported by the Deutsche Forschungsgemeinschaft (DFG) through the project “Game-based Synthesis for Industrial Automation” and the TUM International Graduate School of Science and Engineering (IGSSE).
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Notes
- 1.
While mean-payoff parity games allow to directly combine qualitative and quantitative objects [4], our approach does not require any changes to synthesis of the controller, neither to synthesis itself nor to numerical aspects of the synthesis.
- 2.
Available at https://github.com/jkeiren/paritygame-generator.
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Acknowledgments
We thank Majid Zamani and Matthias Rungger for kindly providing the example for the hybrid controller for our experimental evaluation.
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Meyer, P.J., Luttenberger, M. (2016). Solving Mean-Payoff Games on the GPU. In: Artho, C., Legay, A., Peled, D. (eds) Automated Technology for Verification and Analysis. ATVA 2016. Lecture Notes in Computer Science(), vol 9938. Springer, Cham. https://doi.org/10.1007/978-3-319-46520-3_17
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