The Inconsistent Labelling Problem of Stutter-Preserving Partial-Order Reduction

Abstract

In 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 which formalisms this problem may occur. The impact on practical implementations is limited, since they all compute a correct approximation of the theory.

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

“…As noted before, the condition D1 that we propose is stronger than the version in the literature[38,40] since that one suffers from the inconsistent labelling problem[27,28] which also manifests itself in the parity game setting, as we will demonstrate in Example 2.…”

“…Moreover, using the condition in the setting of parity games may result in games with different winners; see Example 2. In [27], we further explore the consequences of the faulty condition for stubborn-set-based POR techniques that can be found in the literature. We here resort to a strengthened version of condition D1 that does not suffer from these issues.…”

A Detailed Account of The Inconsistent Labelling Problem of Stutter-Preserving Partial-Order Reduction

“…In earlier work [NVW20], we identified the inconsistent labelling problem and investigated the theoretical and practical consequences. As detailed in ibid., the problem is witnessed by a counter-example, which is valid for weak stubborn sets and, with a small modification, in a non-deterministic setting for strong stubborn sets.…”

“…We used this knowledge about formalisms in which the inconsistent labelling problem may manifest itself to determine its impact on related work. The investigation in [NVW20] shows that probably all practical implementations of stubborn sets compute an approximation which resolves the inconsistent labelling problem. Furthermore, POR methods based on the standard independence relation, such as ample sets and persistent sets, are not affected.…”

“…Furthermore, POR methods based on the standard independence relation, such as ample sets and persistent sets, are not affected. The current paper improves on [NVW20] with extended explanation and full proofs. In particular, we introduce each of the existing stubborn set conditions with reworked proofs to aid the reader's intuition.…”