A Formal Framework to Measure the Incompleteness of Abstract Interpretations

Campion, Marco; Urban, Caterina; Dalla Preda, Mila; Giacobazzi, Roberto

doi:10.1007/978-3-031-44245-2_7

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2024

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Cited by 2 publications

References 40 publications

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Quantitative Input Usage Static Analysis

Mazzucato,

Campion,

Urban

2024

Lecture Notes in Computer Science

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Quantitative Input Usage Static Analysis

Mazzucato,

Campion,

Urban

2024

Lecture Notes in Computer Science

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Monotonicity and the Precision of Program Analysis

Campion,

Dalla Preda,

Giacobazzi

et al. 2024

Proc. ACM Program. Lang.

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It is widely known that the precision of a program analyzer is closely related to intensional program properties, namely, properties concerning how the program is written. This explains, for instance, the interest in code obfuscation techniques, namely, tools explicitly designed to degrade the results of program analysis by operating syntactic program transformations. Less is known about a possible relation between what the program extensionally computes, namely, its input-output relation, and the precision of a program analyzer. In this paper we explore this potential connection in an effort to isolate program fragments that can be precisely analyzed by abstract interpretation, namely, programs for which there exists a complete abstract interpretation. In the field of static inference of numeric invariants, this happens for programs, or parts of programs, that manifest a monotone (either non-decreasing or non-increasing) behavior. We first formalize the notion of program monotonicity with respect to a given input and a set of numerical variables of interest. A sound proof system is then introduced with judgments specifying whether a program is monotone relatively to a set of variables and a set of inputs. The interest in monotonicity is justified because we prove that the family of monotone programs admits a complete abstract interpretation over a specific class of non-trivial numerical abstractions and inputs. This class includes all non-relational abstract domains that refine interval analysis (i.e., at least as precise as the intervals abstraction) and that satisfy a topological convexity hypothesis.

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A Formal Framework to Measure the Incompleteness of Abstract Interpretations

Cited by 2 publications

References 40 publications

Quantitative Input Usage Static Analysis

Quantitative Input Usage Static Analysis

Monotonicity and the Precision of Program Analysis

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