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Well-structured transition systems (WSTS's) are a general class of innnite state systems for which decidability results rely on the existence of a well-quasi-ordering between states that is compatible with the transitions. In this article, we provide an extensive treatment of the WSTS idea and show several new results. Our improved deenitions allow many… (More)

Well-structured transition systems provide the right foundation to compute a finite basis of the set of predecessors of the upward closure of a state. The dual problem, to compute a finite representation of the set of successors of the downward closure of a state, is harder: Until now, the theoretical framework for manipulating downward-closed sets was… (More)

- Sébastien Bardin, Alain Finkel, Jérôme Leroux, Laure Petrucci
- 2003

Fast is a tool for the analysis of large or even infinite systems. This paper describes the underlying theory, the architecture choices that have been made in the tool design. The user must provide a model to analyse, the property to check and a computation policy. Several such policies are proposed as a standard in the package, others can be added by the… (More)

We analyze the model-checking problems for safety and liveness properties in parameterized broadcast protocols, a model introduced in [5]. We show that the procedure suggested in [5] for safety properties may not terminate, whereas termination is guaranteed for the procedure of [1] based on upward closed sets. We show that the model-checking problem for… (More)

This paper gives a simple and direct algorithm for computing the always regular set of reachable states of a pushdown system. It then exploits this algorithm for obtaining model checking algorithms for linear-time temporal logic as well as for the logic CTL. For the latter, a new technical tool is introduced: pushdown automata with transitions conditioned… (More)

We describe a simple, conceptual forward analysis procedure for ∞-complete WSTS S. This computes the clover of a state s0, i.e., a finite description of the closure of the cover of s0. When S is the completion of a WSTS X, the clover in S is a finite description of the cover in X. We show that this applies exactly when X is an ω 2-WSTS, a new robust class… (More)

We extend the class of reversal-bounded counter machines by authorizing a finite number of alternations between increasing and decreasing mode over a given bound. We prove that extended reversal-bounded counter machines also have effective semi-linear reachability sets. We also prove that the property of being reversal-bounded is undecidable in general even… (More)