Related papers: A Calculus for Modular Loop Acceleration and Non-T…
Loop acceleration can be used to prove safety, reachability, runtime bounds, and (non-)termination of programs operating on integers. To this end, a variety of acceleration techniques has been proposed. However, all of them are monolithic:…
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…
We present the new version of the Loop Acceleration Tool (LoAT), a powerful tool for proving non-termination and worst-case lower bounds for programs operating on integers. It is based on a novel calculus for loop acceleration, i.e.,…
Bounded Model Checking (BMC) is a powerful technique for proving unsafety. However, finding deep counterexamples that require a large bound is challenging for BMC. On the other hand, acceleration techniques compute "shortcuts" that…
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…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
Infinite-state games provide a framework for the synthesis of reactive systems with unbounded data domains. Solving such games typically relies on computing symbolic fixpoints, particularly symbolic attractors. However, these computations…
Constrained Horn Clauses (CHCs) are often used in automated program verification. Thus, techniques for (dis-)proving satisfiability of CHCs are a very active field of research. On the other hand, acceleration techniques for computing…
We present abstract acceleration techniques for computing loop invariants for numerical programs with linear assignments and conditionals. Whereas abstract interpretation techniques typically over-approximate the set of reachable states…
The calculation of one loop integrals at finite temperature requires the evaluation of certain series, which converge very slowly or can even be divergent. Here we review a new method, recently devised by the author, for obtaining…
We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows to overcome these…
We describe a convergence acceleration technique for unconstrained optimization problems. Our scheme computes estimates of the optimum from a nonlinear average of the iterates produced by any optimization method. The weights in this average…
This article introduces new acceleration methods for fixed-point iterations. Extrapolations are computed using two or three mappings alternately and a new type of step length is proposed with good properties for nonlinear applications. The…
We recently proposed Acceleration Driven Clause Learning (ADCL), a novel calculus to analyze satisfiability of Constrained Horn Clauses (CHCs). Here, we adapt ADCL to disprove termination of transition systems, and we evaluate its…
We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows overcoming these…
This paper presents convergence acceleration, a method for computing efficiently the limit of numerical sequences as a typical application of streams and higher-order functions.
We propose a modular method for proving termination of general logic programs (i.e., logic programs with negation). It is based on the notion of acceptable programs, but it allows us to prove termination in a truly modular way. We consider…
We propose a novel method to compute multi-loop master integrals by constructing and numerically solving a system of ordinary differential equations, with almost trivial boundary conditions. Thus it can be systematically applied to problems…
We present a sequent calculus system for a modal reformulation of a system of nonmonotonic logic due to McCain and Turner: we prove cut elimination for our system. The proof system is in general infinitary: because we can prove cut…
Dynamic logic is a modal logic for reasoning about programs. A cyclic proof system is a proof system that allows proofs containing cycles and is an alternative to a proof system containing (co-)induction. This paper introduces a sequent…