Partial-order reduction for parity games and parameterised Boolean equation systems

Abstract

In model checking, reduction techniques can be helpful tools to fight the state-space explosion problem. Partial-order reduction (POR) is a well-known example, and many POR variants have been developed over the years. However, none of these can be used in the context of model checking stutter-sensitive temporal properties. We propose POR techniques for parity games, a well-established formalism for solving a variety of decision problems, including model checking. As a result, we obtain the first POR method that is sound for the full modal $$\upmu $$ μ -calculus. We show how our technique can be applied to the fixed point logic called parameterised Boolean equation systems, which provides a high-level representation of parity games. Experiments with our implementation indicate that substantial reductions can be achieved.

Partial-Order Reduction for Parity Games with an Application on Parameterised Boolean Equation Systems

“…An encoding of (branching) bisimulation of infinite LTSs in PBES is proposed in [CPvdPW07]. Various procedures that operate on PBES have been studied, for example to simplify [Nee22,OW10] or solve PBES [NWG20, NWWV22,PWW11]. Algorithms for solving some timed fragments of PBES automatically are studied in [ZC05].…”