Stochastic Games with Lexicographic Reachability-Safety Objectives

05/08/2020
by   Krishnendu Chatterjee, et al.
0

We study turn-based stochastic zero-sum games with lexicographic preferences over reachability and safety objectives. Stochastic games are standard models in control, verification, and synthesis of stochastic reactive systems that exhibit both randomness as well as angelic and demonic non-determinism. Lexicographic order allows to consider multiple objectives with a strict preference order over the satisfaction of the objectives. To the best of our knowledge, stochastic games with lexicographic objectives have not been studied before. We establish determinacy of such games and present strategy and computational complexity results. For strategy complexity, we show that lexicographically optimal strategies exist that are deterministic 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 NP ∩ coNP, matching the current known bound for single objectives; and in general the decision problem is PSPACE-hard and can be solved in NEXPTIME ∩ coNEXPTIME. We present an algorithm that computes the lexicographically optimal strategies via a reduction to computation of optimal strategies in a sequence of single-objectives games. We have implemented our algorithm and report experimental results on various case studies.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/22/2022

Strategy Complexity of Reachability in Countable Stochastic 2-Player Games

We study countably infinite stochastic 2-player games with reachability ...
research
08/10/2021

Stochastic Games with Disjunctions of Multiple Objectives (Technical Report)

Stochastic games combine controllable and adversarial non-determinism wi...
research
09/17/2021

Stochastic Games with Disjunctions of Multiple Objectives

Stochastic games combine controllable and adversarial non-determinism wi...
research
05/29/2018

Beyond admissibility: Dominance between chains of strategies

Admissible strategies, i.e. those that are not dominated by any other st...
research
12/22/2022

Playing Safe, Ten Years Later

We consider two-player games over graphs and give tight bounds on the me...
research
05/27/2022

General Optimization Framework for Recurrent Reachability Objectives

We consider the mobile robot path planning problem for a class of recurr...
research
05/26/2021

TEMPEST – Synthesis Tool for Reactive Systems and Shields in Probabilistic Environments

We present Tempest, a synthesis tool to automatically create correct-by-...

Please sign up or login with your details

Forgot password? Click here to reset