Techniques for the efficient successive under-approximation of the greatest fixpoint in TCTL formulas can be useful in fast refutation of inevitability properties and vacuity checking. We first give an integrated algorithmic framework for both under and over-approximate model-checking. We design the NZF (Non-Zeno Fairness) predicate, with a greatest fixpoint formulation, as a unified framework ...

This paper describes a denotational approach to the Petri net semantics of recursive expressions. A domain of nets is identified such that the solution of a given recursive equation can be found by fixpoint approximation from some suitable starting point. In turn, a suitable starting point can be found by fixpoint approximation on a derived domain of sets of trees. The paper explains the theory...

Constraint propagation can sometimes be described conveniently in a rule-based way. Propagation is then fixpoint computation with rules. In the typical case when no specific strategy guides the fixpoint computation, it is preferable to have a minimal set of rules. We propose a natural criterion for redundancy of a rule, and describe a test for a class of rules. Its relevance is demonstrated by ...

The polyadic μ-calculus is a modal fixpoint logic whose formulas define relations of nodes rather than just sets in labelled transition systems. It can express exactly the polynomial-time computable and bisimulation-invariant queries on finite graphs. In this paper we show a hierarchy result with respect to expressive power inside the polyadic μ-calculus: for every level of fixpoint alternation...

We give a new practical algorithm to compute, in finite time, a fixpoint (and often the least fixpoint) of a system of equations in the abstract numerical domains of zones and templates used for static analysis of programs by abstract interpretation. This paper extends previous work on the non-relational domain of intervals to relational domains. The algorithm is based on policy iteration techn...

Static analysis by abstract interpretation aims at automatically proving properties of computer programs, by computing invariants that over-approximate the program behaviors. These invariants are defined as the least fixpoint of a system of semantic equations and are most often computed using Kleene iteration. This computation may not terminate so specific solutions were proposed to deal with t...

In this paper, we address the problem of defining a fixpoint semantics for Constraint Handling Rules (CHR) that captures the behavior of both simplification and propagation rules in a sound and complete way with respect to their declarative semantics. Firstly, we show that the logical reading of states with respect to a set of simplification rules can be characterized by a least fixpoint over t...