Quantitative Reductions and Vertex-Ranked Infinite Games
Abstract
We introduce quantitative reductions, a novel technique for structuring the space of quantitative games and solving them that does not rely on a reduction to qualitative games. We show that such reductions exhibit the same desirable properties as their qualitative counterparts and additionally retain the optimality of solutions. Moreover, we introduce vertex-ranked games as a general-purpose target for quantitative reductions and show how to solve them. In such games, the value of a play is determined only by a qualitative winning condition and a ranking of the vertices. We provide quantitative reductions of quantitative request-response games to vertex-ranked games, thus showing ExpTime-completeness of solving the former games. Furthermore, we exhibit the usefulness and flexibility of vertex-ranked games by showing how to use such games to compute fault-resilient strategies for safety specifications. This work lays the foundation for a general study of fault-resilient strategies for more complex winning conditions
Keywords
Cite
@article{arxiv.1809.03887,
title = {Quantitative Reductions and Vertex-Ranked Infinite Games},
author = {Alexander Weinert},
journal= {arXiv preprint arXiv:1809.03887},
year = {2018}
}
Comments
In Proceedings GandALF 2018, arXiv:1809.02416. arXiv admin note: substantial text overlap with arXiv:1704.00904