2018/09/10 by Alexander Weinert
Computer Science · #cs.GT
paper · pdf · doi:10.4204/eptcs.277.1
published as EPTCS 277, 2018, pp. 1-15 · In Proceedings GandALF 2018, arXiv:1809.02416. arXiv admin note: substantial text overlap with arXiv:1704.00904
arxiv created 2018/09/10 · arxiv updated 2018/09/12
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