Abstract
AbstractWe study turn-based stochastic zero-sum games with lexicographic preferences over objectives. Stochastic games are standard models in control, verification, and synthesis of stochastic reactive systems that exhibit both randomness as well as controllable and adversarial non-determinism. Lexicographic order allows one to consider multiple objectives with a strict preference order. To the best of our knowledge, stochastic games with lexicographic objectives have not been studied before. For a mixture of reachability and safety objectives, we show that deterministic lexicographically optimal strategies exist and memory is only required to remember the already satisfied and violated objectives. For a constant number of objectives, we show that the relevant decision problem is in $$\textsf{NP}\cap \textsf{coNP}$$
NP
∩
coNP
, matching the current known bound for single objectives; and in general the decision problem is $$\textsf{PSPACE}$$
PSPACE
-hard and can be solved in $$\textsf{NEXPTIME}\cap \textsf{coNEXPTIME}$$
NEXPTIME
∩
coNEXPTIME
. We present an algorithm that computes the lexicographically optimal strategies via a reduction to the computation of optimal strategies in a sequence of single-objectives games. For omega-regular objectives, we restrict our analysis to one-player games, also known as Markov decision processes. We show that lexicographically optimal strategies exist and need either randomization or finite memory. We present an algorithm that solves the relevant decision problem in polynomial time. We have implemented our algorithms and report experimental results on various case studies.
Funder
Deutsche Forschungsgemeinschaft
RWTH Aachen University
Publisher
Springer Science and Business Media LLC
Subject
Hardware and Architecture,Theoretical Computer Science,Software
Reference68 articles.
1. Condon A (1992) The complexity of stochastic games. Inf Comput 96(2):203–224. https://doi.org/10.1016/0890-5401(92)90048-K
2. Puterman ML (2014) Markov decision processes: discrete stochastic dynamic programming. Wiley, New Jersey
3. Baier C, Katoen J-P (2008) Principles of model checking. MIT Press, Massachusetts
4. Filar J, Vrieze K (1997) Competitive markov decision processes. Springer, Switzerland
5. Chatterjee K, Henzinger TA (2012) A survey of stochastic $$\omega $$-regular games. J Comput Syst Sci 78(2):394–413. https://doi.org/10.1016/j.jcss.2011.05.002
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