Structural Reductions and Stutter Sensitive Properties

TL;DR

This paper introduces weaker forms of stutter insensitivity, namely shortening and lengthening insensitivity, and develops methods to verify properties using structural reductions even when properties are not fully stutter invariant.

Contribution

It defines new classes of properties (shortening and lengthening insensitive) and proposes semi-decision procedures and reduction techniques for their verification.

Findings

Most non-random stutter-sensitive properties are actually shortening or lengthening insensitive.

Structural reductions like Lipton's transactions can be used with these new property classes.

The approach enables verification of properties beyond traditional stutter invariance.

Abstract

Verification of properties expressed as $\omega$-regular languages such as LTL can benefit hugely from stutter insensitivity, using a diverse set of reduction strategies. However properties that are not stutter invariant, for instance due to the use of the neXt operator of LTL or to some form of counting in the logic, are not covered by these techniques in general. We propose in this paper to study a weaker property than stutter insensitivity. In a stutter insensitive language both adding and removing stutter to a word does not change its acceptance, any stuttering can be abstracted away; by decomposing this equivalence relation into two implications we obtain weaker conditions. We define a shortening insensitive language where any word that stutters less than a word in the language must also belong to the language. A lengthening insensitive language has the dual property. A semi-decision procedure is then introduced to reliably prove shortening insensitive properties or deny lengthening insensitive properties while working with a \emph{reduction} of a system. A reduction has the property that it can only shorten runs. Lipton's transaction reductions or Petri net agglomerations are examples of eligible structural reduction strategies. We also present an approach that can reason using a partition of a property language into its stutter insensitive, shortening insensitive, lengthening insensitive and length sensitive parts to still use structural reductions even when working with arbitrary properties. An implementation and experimental evidence is provided showing most non-random properties sensitive to stutter are actually shortening or lengthening insensitive.