An Abstract Domain to Infer Ordinal-Valued Ranking Functions

Urban, Caterina; Miné, Antoine

doi:10.1007/978-3-642-54833-8_22

Cited by 38 publications

(49 citation statements)

References 25 publications

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“…A ranking function is a standard proof method in such a setting. There are variations in the definition of ranking function [4], [20], [21]: in this paper we use the following.…”

Section: A Two-player Games and Ranking Functionsmentioning

confidence: 99%

Categorical liveness checking by corecursive algebras

Urabe

Hara

Hasuo

2017

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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Abstract-Final coalgebras as "categorical greatest fixed points" play a central role in the theory of coalgebras. Somewhat analogously, most proof methods studied therein have focused on greatest fixed-point properties like safety and bisimilarity. Here we make a step towards categorical proof methods for least fixed-point properties over dynamical systems modeled as coalgebras. Concretely, we seek a categorical axiomatization of well-known proof methods for liveness, namely ranking functions (in nondeterministic settings) and ranking supermartingales (in probabilistic ones). We find an answer in a suitable combination of coalgebraic simulation (studied previously by the authors) and corecursive algebra as a classifier for (non-)well-foundedness.

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“…A ranking function is a standard proof method in such a setting. There are variations in the definition of ranking function [4], [20], [21]: in this paper we use the following.…”

Section: A Two-player Games and Ranking Functionsmentioning

confidence: 99%

Categorical liveness checking by corecursive algebras

Urabe

Hara

Hasuo

2017

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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“…Ranking functions can also be computed via abstract interpretation [CC12]. Urban and Miné [Urb13,UM14a,UM14b] introduced the domain of piecewise defined ordinalvalued functions for this approach. In contrast to our work, their approach is applicable to programs with arbitrary structure and not restricted to linear lasso programs.…”

Section: Related Workmentioning

confidence: 99%

Ranking Templates for Linear Loops

Leike¹,

Heizmann²

2015

Logical Methods in Computer Science

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Abstract. We present a new method for the constraint-based synthesis of termination arguments for linear loop programs based on linear ranking templates. Linear ranking templates are parameterized, well-founded relations such that an assignment to the parameters gives rise to a ranking function. Our approach generalizes existing methods and enables us to use templates for many different ranking functions with affine-linear components. We discuss templates for multiphase, nested, piecewise, parallel, and lexicographic ranking functions. These ranking templates can be combined to form more powerful templates. Because these ranking templates require both strict and non-strict inequalities, we use Motzkin's transposition theorem instead of Farkas' lemma to transform the generated ∃∀-constraint into an ∃-constraint.

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“…The fundamental concept in the theory of abstract interpretation is the abstract domain, a mathematical representation of program properties equipped with a set of operators. Over the last few decades, the research community has developed a wide range of abstract domains targeting a diverse set of important program properties including heap [26,28], numerical properties [12,20,22,23], termination [29,30] and many others. In this work we focus on numerical domains, which are at the core of any modern static analyzer [6-8, 13, 24, 25].…”

Section: Introductionmentioning

confidence: 99%

Making numerical program analysis fast

Singh

Püschel

Vechev

2015

Proceedings of the 36th ACM SIGPLAN Conference on Programming Language Design and Implementation

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Numerical abstract domains are a fundamental component in modern static program analysis and are used in a wide range of scenarios (e.g. computing array bounds, disjointness, etc). However, analysis with these domains can be very expensive, deeply affecting the scalability and practical applicability of the static analysis. Hence, it is critical to ensure that these domains are made highly efficient.In this work, we present a complete approach for optimizing the performance of the Octagon numerical abstract domain, a domain shown to be particularly effective in practice. Our optimization approach is based on two key insights: i) the ability to perform online decomposition of the octagons leading to a massive reduction in operation counts, and ii) leveraging classic performance optimizations from linear algebra such as vectorization, locality of reference, scalar replacement and others, for improving the key bottlenecks of the domain. Applying these ideas, we designed new algorithms for the core Octagon operators with better asymptotic runtime than prior work and combined them with the optimization techniques to achieve high actual performance. We implemented our approach in the Octagon operators exported by the popular APRON C library, thus enabling existing static analyzers using APRON to immediately benefit from our work.To demonstrate the performance benefits of our approach, we evaluated our framework on four published static analyzers showing massive speedups for the time spent in Octagon analysis (e.g., up to 146x) as well as significant end-to-end program analysis speedups (up to 18.7x). Based on these results, we believe that our framework can serve as a new basis for static analysis with the Octagon numerical domain.

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An Abstract Domain to Infer Ordinal-Valued Ranking Functions

Cited by 38 publications

References 25 publications

Categorical liveness checking by corecursive algebras

Categorical liveness checking by corecursive algebras

Ranking Templates for Linear Loops

Making numerical program analysis fast

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