Related papers: Proving Non-Termination via Loop Acceleration

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.,…

Loop acceleration can be used to prove safety, reachability, runtime bounds, and (non-)termination of programs. To this end, a variety of acceleration techniques has been proposed. However, so far all of them have been monolithic, i.e., a…

We present a new approach to proving non-termination of non-deterministic integer programs. Our technique is rather simple but efficient. It relies on a purely syntactic reversal of the program's transition system followed by a…

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:…

A new technique is presented to prove non-termination of term rewriting. The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms. It is automated by representing the…

We present a static analysis technique for non-termination inference of logic programs. Our framework relies on an extension of the subsumption test, where some specific argument positions can be instantiated while others are generalized.…

In this paper, we consider an approach introduced in term rewriting for the automatic detection of non-looping non-termination from patterns of rules. We adapt it to logic programming by defining a new unfolding technique that produces…

We describe a method for proving non-looping non-termination, that is, of term rewriting systems that do not admit looping reductions. As certificates of non-termination, we employ regular (tree) automata.

Loop invariants play a central role in the verification of imperative programs. However, finding these invariants is often a difficult and time-consuming task for the programmer. We have previously shown how program transformation can be…

In the past years, analyzers have been introduced to detect classes of non-terminating queries for definite logic programs. Although these non-termination analyzers have shown to be rather precise, their applicability on real-life Prolog…

We describe the LoopInvGen tool for generating loop invariants that can provably guarantee correctness of a program with respect to a given specification. LoopInvGen is an efficient implementation of the inference technique originally…

Proving program termination is typically done by finding a well-founded ranking function for the program states. Existing termination provers typically find ranking functions using either linear algebra or templates. As such they are often…

There is growing interest in termination reasoning for non-linear programs and, meanwhile, recent dynamic strategies have shown they are able to infer invariants for such challenging programs. These advances led us to hypothesize that…

We introduce a fully automated static analysis that takes a sequential Java bytecode program P as input and attempts to prove that there exists an infinite execution of P. The technique consists in compiling P into a constraint logic…

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 present a technique to infer lower bounds on the worst-case runtime complexity of integer programs, where in contrast to earlier work, our approach is not restricted to tail-recursion. Our technique constructs symbolic representations of…

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…

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 report on our tool, Pulse Infinite, that uses proof techniques to show non-termination (divergence) in large programs. Pulse Infinite works compositionally and under-approximately: the former supports scale, and the latter ensures…

We consider the termination/non-termination property of a class of loops. Such loops are commonly used abstractions of real program pieces. Second-order logic is a convenient language to express non-termination. Of course, such property is…