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Proving the termination of a flowchart program can be done by exhibiting a ranking function, i.e., a function from the program states to a well-founded set, which strictly decreases at each program step. A standard method to automatically generate such a function is to compute invariants for each program point and to search for a ranking in a restricted(More)
Linear Relation Analysis [CH78,Hal79] is one of the first, but still one of the most powerful, abstract interpretations working in an infinite lattice. As such, it makes use of a widening operator to enforce the convergence of fixpoint computations. While the approximation due to widening can be arbitrarily refined by delaying the application of widening,(More)
Recent work on component-based software design has proved the need of resource-accurate development of embedded software. In the more specific cases of mobile systems, the developer also needs tools to facilitate the adaptation of functionalities to resources (lack of memory or bandwidth, etc.), and also to evaluate the performance w.r.t. the resource(More)
In this paper, we present Aspic, an automatic polyhedral invariant generation tool for flowcharts programs. Aspic implements an improved Linear Relation Analysis on numeric counter automata. The " accelerated " method improves precision by computing locally a precise overapproximation of a loop without using the widening operator. c2fsm is a C preprocessor(More)
Convex polyhedra are often used to approximate sets of states of programs involving numerical variables. The manipulation of convex polyhedra relies on the so-called double description, consisting of viewing a polyhedron both as the set of solutions of a system of linear inequalities, and as the convex hull of a system of generators, i.e., a set of vertices(More)
In this paper, we propose a sound abstraction for an efficient static analysis of synchronous programs describing multi-clock embedded systems in Signal. This abstraction combines the Boolean theory and numeric interval approximation to adequately address clock relations defined as combinations of logical and numerical expressions. Through a few examples,(More)
Linear Relation Analysis [28, 39] is now a classical abstract interpretation based on an approximation of reachable numerical states of a program by convex polyhedra. Since it works with a lattice of infinite depth, it makes use of a widening operator to enforce the convergence of fixpoint computations. This paper takes place in the many attempts to improve(More)