Disproving termination with overapproximation

Cook, Byron; Fuhs, Carsten; Nimkar, Kaustubh; O’Hearn, Peter W.

doi:10.1109/fmcad.2014.6987597

Cited by 23 publications

(36 citation statements)

References 33 publications

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“…LoAT The TPDB examples mostly use linear arithmetic and T2 and VeryMax are restricted to such programs [11,32]. To evaluate LoAT on examples with non-linear arithmetic, we also compared with the tool Anant [14], which has been specifically designed to handle non-linearity. Here, we used the 29 non-terminating programs with non-linear arithmetic from the evaluation of [14].…”

Section: Methodsmentioning

confidence: 99%

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Proving Non-Termination via Loop Acceleration

Frohn

Giesl

2019

2019 Formal Methods in Computer Aided Design (FMCAD)

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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 non-terminating loops automatically. The prerequisites for our novel loop acceleration technique generalize a simple yet effective non-termination criterion. Thus, we can use the same program transformations to facilitate both non-termination proving and loop acceleration. In particular, we present a novel invariant inference technique that is tailored to our approach. An extensive evaluation of our fully automated tool LoAT shows that it is competitive with the state of the art.

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Section: Methodsmentioning

confidence: 99%

“…Proving non-termination of integer programs is an important research topic (e.g., [2,7,13,14,26,32,33,34,39,40]). In another line of research, under-approximating loop acceleration is used to analyze safety [30] and runtime complexity [21].…”

Section: Introductionmentioning

confidence: 99%

Proving Non-Termination via Loop Acceleration

Frohn

Giesl

2019

2019 Formal Methods in Computer Aided Design (FMCAD)

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“…Traditional algorithms, e.g. [3,6,8,20,22], are based on a search for lasso-shaped traces and a discovery of recurrence sets, i.e., states that are visited infinitely often. For instance, [32] searches for a geometric series in lasso-shaped traces.…”

Section: Related Workmentioning

confidence: 99%

Syntax-Guided Termination Analysis

Fedyukovich

Zhang

Gupta

2018

Computer Aided Verification

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Abstract. We present new algorithms for proving program termination and non-termination using syntax-guided synthesis. They exploit the symbolic encoding of programs and automatically construct a formal grammar for symbolic constraints that are used to synthesize either a termination argument or a non-terminating program refinement. The constraints are then added back to the program encoding, and an offthe-shelf constraint solver decides on their fitness and on the progress of the algorithms. The evaluation of our implementation, called FreqTerm, shows that although the formal grammar is limited to the syntax of the program, in the majority of cases our algorithms are effective and fast. Importantly, FreqTerm is competitive with state-of-the-art on a wide range of terminating and non-terminating benchmarks, and it significantly outperforms state-of-the-art on proving non-termination of a class of programs arising from large-scale Event-Condition-Action systems.

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“…That is, they find a set of states from which a program cannot escape. This can be done using Farkas' lemma [14], forward [8] or backward [34] abstract interpretation based analysis, or by encoding the search as a max-SMT problem [26]. Le et al propose a specification logic and an inference algorithm [27] (implemented in HipTNT+) that can capture the absence of terminating behaviors.…”

Section: Related Workmentioning

confidence: 99%

“…Several modern analyses [8,13,14,26] characterize non-terminating behaviors with a notion of recurrent set, i.e., a set of states from which an execution of the program or fragment cannot or might not escape (there exist multiple definitions). In this paper, we focus on the notion of an existential recurrent set -a set of states, s.t., from every state in the set there exists at least one non-terminating execution.…”

Section: Introductionmentioning

confidence: 99%

Finding Recurrent Sets with Backward Analysis and Trace Partitioning

Bakhirkin

Piterman

2016

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract.We propose an abstract-interpretation-based analysis for recurrent sets. A recurrent set is a set of states from which the execution of a program cannot or might not (as in our case) escape. A recurrent set is a part of a program's nontermination proof (that needs to be complemented by reachability analysis). We find recurrent sets by performing a potentially over-approximate backward analysis that produces an initial candidate. We then perform over-approximate forward analysis on the candidate to check and refine it and ensure soundness. In practice, the analysis relies on trace partitioning that predicts future paths through the program that non-terminating executions will take. Using our technique, we were able to find recurrent sets in many benchmarks found in the literature including some that, to our knowledge, cannot be handled by existing tools. In addition, we note that typically, analyses that search for recurrent sets are applied to linear under-approximations of programs or employ some form of non-approximate numeric reasoning. In contrast, our analysis uses standard abstract-interpretation techniques and is potentially applicable to a larger class of abstract domains (and therefore -programs).

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Disproving termination with overapproximation

Cited by 23 publications

References 33 publications

Proving Non-Termination via Loop Acceleration

Proving Non-Termination via Loop Acceleration

Syntax-Guided Termination Analysis

Finding Recurrent Sets with Backward Analysis and Trace Partitioning

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