Related papers: Abstract Acceleration of General Linear Loops
Linear Time Invariant (LTI) systems are ubiquitous in control applications. Unbounded-time reachability analysis that can cope with industrial-scale models with thousands of variables is needed. To tackle this problem, we use abstract…
We propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and…
We propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and…
We propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and…
Abstraction (in its various forms) is a powerful established technique in model-checking; still, when unbounded data-structures are concerned, it cannot always cope with divergence phenomena in a satisfactory way. Acceleration is an…
Acceleration in symbolic verification consists in computing the exact effect of some control-flow loops in order to speed up the iterative fix-point computation of reachable states. Even if no termination guarantee is provided in theory,…
In this paper, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving a sequence of linear programs, resulting in a sequence of affine upper and lower hyperplanes…
Static analysis by abstract interpretation aims at automatically proving properties of computer programs. To do this, an over-approximation of program semantics, defined as the least fixpoint of a system of semantic equations, must be…
Abstract interpretation techniques can be made more precise by distinguishing paths inside loops, at the expense of possibly exponential complexity. SMT-solving techniques and sparse representations of paths and sets of paths avoid this…
The inference and the verification of numerical relationships among variables of a program is one of the main goals of static analysis. In this paper, we propose an Abstract Interpretation framework based on higher-dimensional ellipsoids to…
Approximations during program analysis are a necessary evil, as they ensure essential properties, such as soundness and termination of the analysis, but they also imply not always producing useful results. Automatic techniques have been…
We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be…
We propose a novel acceleration technique for loops operating on arrays. The goal of acceleration is to characterize the transitive closure of loops in a logic which is suitable for automated reasoning. Using the new notion of inductive…
We present the first approach to prove non-termination of integer programs that is based on loop acceleration. If our technique cannot show non-termination of a loop, it tries to accelerate it instead in order to find paths to other…
The traditional abstract domain framework for imperative programs suffers from several shortcomings; in particular it does not allow precise symbolic abstractions. To solve these problems, we propose a new abstract interpretation framework,…
We consider the problem of computing numerical invariants of programs, for instance bounds on the values of numerical program variables. More specifically, we study the problem of performing static analysis by abstract interpretation using…
We consider the problem of computing numerical invariants of programs by abstract interpretation. Our method eschews two traditional sources of imprecision: (i) the use of widening operators for enforcing convergence within a finite number…
We present and evaluate a technique for computing path-sensitive interference conditions during abstract interpretation of concurrent programs. In lieu of fixed point computation, we use prime event structures to compactly represent causal…
We present a novel approach for generalizing the IC3 algorithm for invariant checking from finite-state to infinite-state transition systems, expressed over some background theories. The procedure is based on a tight integration of IC3 with…
In this paper we propose a novel methodology for static analysis of binary code using abstract interpretation. We use an abstract domain based on polyhedra and two mapping functions that associate polyhedra variables with registers and…