Laure Gonnord

Using bounded model checking to focus fixpoint iterations

Two classical sources of imprecision in static analysis by abstract interpretation are widening and merge operations. Merge operations can be done away by distinguishing paths, as in trace partitioning, at the expense of enumerating an exponential number of paths. n nIn this article, we describe how to avoid such systematic exploration by focusing on a single path at a time, designated by SMT-solving. Our method combines well with acceleration techniques, thus doing away with widenings as well in some cases. We illustrate it over the well-known domain of convex polyhedra.

Accelerated Invariant Generation for C Programs with Aspic and C2fsm

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 that generates automata in the format required by Aspic. The experimental results show the performance and precision of the tools.

Abstract acceleration in linear relation analysis

Linear relation analysis is a classical abstract interpretation based on an over-approximation of reachable numerical states of a program by convex polyhedra. Since it works with a lattice of infinite height, it makes use of a widening operator to enforce the convergence of fixed point computations. Abstract acceleration is a method that computes the precise abstract effect of loops wherever possible and uses widening in the general case. Thus, it improves both the precision and the efficiency of the analysis. This article gives a comprehensive tutorial on abstract acceleration: its origins in Presburger-based acceleration including new insights w.r.t. the linear accelerability of linear transformations, methods for simple and nested loops, recent extensions, tools and applications, and a detailed discussion of related methods and future perspectives.

Rank: A Tool to Check Program Termination and Computational Complexity

Summary form only given. 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 that strictly decreases at each program step. In a previous paper , we proposed an algorithm to compute multidimensional affine ranking functions for flowcharts of arbitrary structure. Our method, although greedy, is provably complete for the class of rankings we consider. The ranking functions we generate can also be used to get upper bounds for the computational complexity (number of transitions) of the source program. This estimate is a polynomial, which means that we can handle programs with more than linear complexity. This abstract aims at presenting RANK, the tool that implements our algorithm.