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.

Verification of properties expressed as-regular languages such as LTL can benefit hugely from stutter-insensitivity, using a diverse set of reduction strategies. However properties that are not stutter-insensitive, 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 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. An implementation and experimental evidence is provided showing most nonrandom properties sensitive to stutter are actually shortening or lengthening insensitive. Performance of experiments on a large (random) benchmark from the model-checking competition indicate that despite being a semi-decision procedure, the approach can still improve state of the art verification tools.

We propose a new model of branching processes, suitable for describing the behavior of general Petri nets, without any finiteness or safeness assumption. In this framework, we define a new class of branching processes and unfoldings of a net N, which

Recursive Petri nets (RPNs) have been introduced to model systems with dynamic structure. Whereas this model is a strict extension of Petri nets and context-free grammars (w.r.t. the language criterion), reachability in RPNs remains decidable. However the kind of model checking which is decidable for Petri nets becomes undecidable for RPNs. In this paper, we introduce a submodel of RPNs called sequential recursive Petri nets (SRPNs) and we study the model checking of the action-based linear time logic on SRPNs. We prove that it is decidable for all its variants: finite sequences, finite maximal sequences, infinite sequences and divergent sequences. At the end, we analyze language aspects proving that the SRPN languages still strictly include the union of Petri nets and context-free languages and that the family of languages of SRPNs is closed under intersection with regular languages (unlike the one of RPNs).