Verification of Source Code Transformations by Program Equivalence Checking

Shashidhar, K. C.; Bruynooghe, Maurice; Catthoor, Francky; Janssens, Gerda

doi:10.1007/978-3-540-31985-6_15

Cited by 26 publications

(30 citation statements)

References 15 publications

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“…Recurrence Equivalence Barthou et al [6] and Shashidhar et al [40] present different algorithms to prove the equivalence of systems of affine recurrence equations that are structurally similar. Verdoolaege et al [45] propose an algorithm to prove the equivalence of integer affine programs where loops are described as recurrences.…”

Section: Related Workmentioning

confidence: 99%

Automatic Equivalence Checking of UF+IA Programs

Lopes

Monteiro

2013

Model Checking Software

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Abstract. Proving the equivalence of programs has several important applications, including algorithm recognition, regression checking, compiler optimization verification, and information flow checking. Despite being a topic with so many important applications, program equivalence checking has seen little advances over the past decades due to its inherent (high) complexity. In this paper, we propose, to the best of our knowledge, the first algorithm for the automatic verification of partial equivalence of two programs over the combined theory of uninterpreted function symbols and integer arithmetic (UF+IA). The proposed algorithm supports, in particular, programs with nested loops. The crux of the technique is a transformation of uninterpreted functions (UFs) applications into integer polynomials, which enables the summarization of loops with UF applications using recurrences. The equivalence checking algorithm then proceeds on loop-free, integer only programs. We implemented the proposed technique in CORK, a tool that automatically verifies the correctness of compiler optimizations, and we show that it can prove more optimizations correct than state-of-the-art techniques.

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Section: Related Workmentioning

confidence: 99%

Automatic Equivalence Checking of UF+IA Programs

Lopes

Monteiro

2013

Model Checking Software

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“…In this section, we introduce a program model that captures exactly this information. Unlike [20,21] where an array based representation is used and some dependence analysis is implicitly performed during the equivalence checking, we separate the dependence analysis from the equivalence checking, the latter working on the output of the former. This separation allows us to use standard exact dataflow analysis [10] or, in future work, fuzzy dataflow analysis [5].…”

Section: Program Modelmentioning

confidence: 99%

“…The equivalence checking of static affine programs has been previously investigated by Barthou et al [1,6] and Shashidhar et al [20,21]. A major challenge in this line of research is posed by recurrences, i.e., a statement in a loop that (indirectly) depends on previous iterations of the same statement.…”

Section: Introductionmentioning

confidence: 99%

Equivalence checking of static affine programs using widening to handle recurrences

Verdoolaege

Janssens

Bruynooghe

2012

ACM Trans. Program. Lang. Syst.

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Abstract. Designers often apply manual or semi-automatic loop and data transformations on array and loop intensive programs to improve performance. The transformations should preserve the functionality, however, and this paper presents an automatic method for constructing equivalence proofs for the class of static affine programs. The equivalence checking is performed on a dependence graph abstraction and uses a new approach based on widening to handle recurrences. Unlike transitive closure based approaches, this widening approach can also handle non-uniform recurrences. The implementation is publicly available and is the first of its kind to fully support commutative operations.

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“…Checking program equivalence for sequential programs has been studied in [31,12]. There is a large body of research on checking correctness of parallel programs (e.g., see [14,21,24,17,18,22] and [27] for a survey of more recent work).…”

Section: Related Workmentioning

confidence: 99%

Checking Equivalence of SPMD Programs Using Non-Interference

Tripakis

Stergiou

Lublinerman

2010

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Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. We study one of the basic multicore and GPU programming models, namely, SPMD (Single-Program Multiple-Data) programs. We define a formal model of SPMD programs based on interleaving threads that manipulate global and local arrays, and synchronize via barriers. SPMD programs are written with the intention to be deterministic, although programming errors may result in this not being true. SPMD programs are also frequently modified toward optimal performance. These facts motivate us to develop methods to check determinism and equivalence. A key property in achieving this is noninterference formulated as validity of logical formulas automatically derived from the program, that imply determinism. Automatically derived post-conditions can be used to check equivalence of noninterfering programs. We report on a prototype that can prove non-interference of NVIDIA CUDA programs. Copyright © 2010, by the author(s).All rights reserved.Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission. This work is dedicated to the memory of Amir Pnueli. AbstractWe study one of the basic multicore and GPU programming models, namely, SPMD (Single-Program Multiple-Data) programs. We define a formal model of SPMD programs based on interleaving threads that manipulate global and local arrays, and synchronize via barriers. SPMD programs are written with the intention to be deterministic, although programming errors may result in this not being true. SPMD programs are also frequently modified toward optimal performance. These facts motivate us to develop methods to check determinism and equivalence. A key property in achieving this is noninterference, formulated as validity of logical formulas automatically derived from the program, that imply determinism. Automatically derived post-conditions can be used to check equivalence of noninterfering programs. We report on a prototype that can prove non-int...

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Verification of Source Code Transformations by Program Equivalence Checking

Cited by 26 publications

References 15 publications

Automatic Equivalence Checking of UF+IA Programs

Automatic Equivalence Checking of UF+IA Programs

Equivalence checking of static affine programs using widening to handle recurrences

Checking Equivalence of SPMD Programs Using Non-Interference

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