Abstraction Refinement for Games with Incomplete Information

Abstract

Counterexample-guided abstraction refinement (CEGAR) is used in
automated software analysis to find suitable finite-state abstractions
of infinite-state systems.  In this paper, we extend CEGAR to games
with incomplete information, as they commonly occur in controller
synthesis and modular verification. The challenge is that, under
incomplete information, one must carefully account for the knowledge
available to the player: the strategy must not depend on information
the player cannot see. We propose an abstraction mechanism for games under
incomplete information that incorporates the approximation of the players\' moves
into a knowledge-based subset construction on the abstract state
space. This abstraction results in a perfect-information game over a
finite graph. The concretizability of abstract strategies can be encoded as
the satisfiability of strategy-tree formulas. Based on this encoding,
we present an interpolation-based approach for selecting new predicates
and provide sufficient conditions for the termination of the resulting
refinement loop.