Partial-order reduction for parity games and parameterised Boolean equation systems
AbstractIn 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 pro…
The Inconsistent Labelling Problem of Stutter-Preserving Partial-Order Reduction
AbstractIn model checking, partial-order reduction (POR) is an effective technique to reduce the size of the state space. Stubborn sets are an established variant of POR and have seen many applications over the past 31 years. One of the early works on stubborn sets shows that a combination of several conditions on the reduction is sufficient to preserve stutter-trace equivalence, making stubborn sets suitable for model checking of linear-time properties. In this paper, we identify a flaw in the reasoning and show with a counter-example that stutter-trace equivalence is not necessarily preserved. We propose a solution together with an updated correctness proof. Furthermore, we analyse in whi…
A Detailed Account of The Inconsistent Labelling Problem of Stutter-Preserving Partial-Order Reduction
One of the most popular state-space reduction techniques for model checking is partial-order reduction (POR). Of the many different POR implementations, stubborn sets are a very versatile variant and have thus seen many different applications over the past 32 years. One of the early stubborn sets works shows how the basic conditions for reduction can be augmented to preserve stutter-trace equivalence, making stubborn sets suitable for model checking of linear-time properties. In this paper, we identify a flaw in the reasoning and show with a counter-example that stutter-trace equivalence is not necessarily preserved. We propose a stronger reduction condition and provide extensive new correc…