Structural Reductions Revisited

Abstract

Structural reductions are a powerful class of techniques that reason on a specification with the goal to reduce it before attempting to explore its behaviors. In this paper we present new structural reduction rules for verification of deadlock freedom and safety properties of Petri nets. These new rules are presented together with a large body of rules found in diverse literature. For some rules we leverage an SMT solver to compute if application conditions are met. We use a CEGAR approach based on progressively refining the classical state equation with new constraints, and memory-less exploration to confirm counterexamples. Extensive experimentation demonstrates the usefulness of this structural verification approach.

LTL under reductions with weaker conditions than stutter-invariance

“…However, it selects as representative a run involving both 𝑡 1 and 𝑡 2 that is longer than the one using 𝑡 in the original net, it is thus not legitimate to use in our strategy (although it remains valid for 𝐿𝑇 𝐿 \𝑋 ). Rules 14 "Pre agglomeration" and 15 "Post agglomeration" are the most powerful rules of [22] that we are able to apply in our context. They are known to preserve 𝐿𝑇 𝐿 \𝑋 (but not full LTL) and their effect is a reduction at the language level, hence we can use them when dealing with shortening/lengthening insensitive formulae.…”

“…Hence chaining reduction rules still produces a reduction. As we will discuss in section 3.1 structural reductions of a specification such as Lipton's transaction reduction [14,13] or Petri net agglomerations [1,22] induce a reduction at the language level.…”

“…More powerful variants of Berthelot's rules have been defined e.g. in [19,6,9,22] for Petri nets, and for a "modern" overview of Lipton's transaction reductions see [13]. For lack of space, in this paper we decided not to provide proofs that these structural transformation rules induce reductions at the language level.…”

“…Our experimental section 4.2 uses the rules of [22] for (potentially partial) pre and post-agglomeration. That paper presents 22 structural reductions rules from which we selected the rules valid in the context of LTL verification.…”

“…Structural reductions in the literature. The structural reductions rules we used in the performance evaluation are defined on Petri nets where the literature on the subject is rich [1,19,6,9,2,22]. However there are other formalism where similar reduction rules have been defined such as [16] using "atomic" blocks in Promela, transaction reductions for the widely encompassing intermediate language PINS of LTSmin [13], and even in the context of multi-threaded programs [7].…”