On Program Equivalence with Reductions

Iooss, Guillaume; Alias, Christophe; Rajopadhye, Sanjay

doi:10.1007/978-3-319-10936-7_11

Cited by 8 publications

(7 citation statements)

References 22 publications

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“…They do not optimize for complexities; however, they can be used as optimizing backends for generating efficient code for reductions after applying our method. Iooss et al [2014] proposed a semi-algorithm that decides equivalence between programs with reductions; it can be used to check correctness of a program transformation. Simplifying Reductions Liu et al [2005] introduced a loop based transformation algorithm for reducing complexities on loop programs.…”

Section: Related Workmentioning

confidence: 99%

Simplifying dependent reductions in the polyhedral model

Yang

Atkinson

Carbin

2021

Proc. ACM Program. Lang.

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A Reduction – an accumulation over a set of values, using an associative and commutative operator – is a common computation in many numerical computations, including scientific computations, machine learning, computer vision, and financial analytics. Contemporary polyhedral-based compilation techniques make it possible to optimize reductions, such as prefix sums, in which each component of the reduction’s output potentially shares computation with another component in the reduction. Therefore an optimizing compiler can identify the computation shared between multiple components and generate code that computes the shared computation only once. These techniques, however, do not support reductions that – when phrased in the language of the polyhedral model – span multiple dependent statements. In such cases, existing approaches can generate incorrect code that violates the data dependences of the original, unoptimized program. In this work, we identify and formalize the optimization of dependent reductions as an integer bilinear program. We present a heuristic optimization algorithm that uses an affine sequential schedule of the program to determine how to simplfy reductions yet still preserve the program’s dependences. We demonstrate that the algorithm provides optimal complexity for a set of benchmark programs from the literature on probabilistic inference algorithms, whose performance critically relies on simplifying these reductions. The complexities for 10 of the 11 programs improve siginifcantly by factors at least of the sizes of the input data, which are in the range of 10 4 to 10 6 for typical real application inputs. We also confirm the significance of the improvement by showing speedups in wall-clock time that range from 1.1x to over 10 6 x.

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Section: Related Workmentioning

confidence: 99%

Simplifying dependent reductions in the polyhedral model

Yang

Atkinson

Carbin

2021

Proc. ACM Program. Lang.

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“…The idea of utilizing program equivalence checking in order to identify quantum algorithms is an unexplored topic. However, program equivalence itself is a well-known and researched topic with numerous applications, including algorithm recognition, program verification, program optimization, and compiler optimization [1] [5]. The term "semantic equivalence" may be used to describe programs that are equivalent: even if written differently, they have the same meaning.…”

Section: Related Workmentioning

confidence: 99%

“…The equivalence problem is said to be undecidable "as soon as the considered program class is rich enough to be interesting" [5]. However, it has been formally shown that the equivalence problem is decidable in simple cases [7].…”

Section: Related Workmentioning

confidence: 99%

Program Equivalence Checking for the Facilitation of Quantum Offloading

Speer

Nurminen

2021

2021 IEEE 11th Annual Computing and Communication Workshop and Conference (CCWC)

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Computational offloading involves the transfer of computational tasks to a separate device. We apply this concept to quantum computing, whereby particular algorithms (i.e. "quantum algorithms") are automatically recognized and executed on a quantum computer. We propose a method that utilizes program equivalence checking to discern between code suited for execution on a conventional computer and a quantum computer. This process involves comparing a quantum algorithm's implementation with code written by a programmer, with semantic equivalence between the two implying that the programmer's code should be executed on a quantum computer instead of a conventional computer. Using a novel compiler optimization verification tool named CORK, we test for semantic equivalence between a portion of Shor's algorithm (the "prototype") and various modified versions of this code (representing the arbitrary code written by a programmer). Some of the modified versions are intended to be semantically equivalent to the prototype while others semantically inequivalent. Our approach is able to correctly determine semantic equivalence or semantic inequivalence in a majority of cases.

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“…Algorithms for proving program equivalence restricted to specific classes of programs have been developed [34]- [37]. These approaches are typically restricted to proving the equivalence of different schedules of operations, possibly via abstract interpretation [38], [39] or even dynamically [40].…”

Section: Static Program Equivalencementioning

confidence: 99%

Self-Supervised Learning to Prove Equivalence Between Programs via Semantics-Preserving Rewrite Rules

Kommrusch¹,

Monperrus²,

Pouchet³

2021

Preprint

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We target the problem of synthesizing proofs of semantic equivalence between two programs made of sequences of statements with complex symbolic expressions. We propose a neural network architecture based on the transformer to generate axiomatic proofs of equivalence between program pairs. We generate expressions which include scalars and vectors and support multi-typed rewrite rules to prove equivalence. For training the system, we develop an original training technique, which we call self-supervised sample selection. This incremental training improves the quality, generalizability and extensibility of the learned model. We study the effectiveness of the system to generate proofs of increasing length, and we demonstrate how transformer models learn to represent complex and verifiable symbolic reasoning. Our system, S4Eq, achieves 97% proof success on 10,000 pairs of programs while ensuring zero false positives by design.

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On Program Equivalence with Reductions

Cited by 8 publications

References 22 publications

Simplifying dependent reductions in the polyhedral model

Simplifying dependent reductions in the polyhedral model

Program Equivalence Checking for the Facilitation of Quantum Offloading

Self-Supervised Learning to Prove Equivalence Between Programs via Semantics-Preserving Rewrite Rules

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