The Compositional Method and Regular Reachability

The Compositional Method and Regular Reachability

The compositional method, introduced by Feferman and Vaught in 1959, allows to reduce the model-checking problem for a product structure to the model-checking problem for its factors. It applies to first-order logic, and limitations for its use have recently been revealed by Rabinovich (2007). We sharpen the results of Rabinovich by showing that the composition method is applicable to the async...

Compositional Reachability in Petri Nets

We introduce a divide-and-conquer algorithm for a modified version of the reachability/coverability problem in 1-bounded Petri nets that relies on the compositional algebra of nets with boundaries: we consider the algebraic decomposition of the net of interest as part of the input. We formally prove the correctness of the technique and contrast the performance of our implementation with state-o...

Compositional Reachability Analysis of Genetic Networks

Genetic regulatory networks have been modeled as discrete transition systems by many approaches, benefiting from a large number of formal verification algorithms available for the analysis of discrete transition systems. However, most of these approaches do not scale up well. In this article, we explore the use of compositionality for the analysis of genetic regulatory networks. We present a fr...

Compositional specification and reachability checking of net systems

Recurrent Reachability Analysis in Regular Model Checking

We consider the problem of recurrent reachability over infinite systems given by regular relations on words and trees, i.e, whether a given regular set of states can be reached infinitely often from a given initial state in the given transition system. Under the condition that the transitive closure of the transition relation is regular, we show that the problem is decidable, and the set of all...