Automatic inversion generates divide-and-conquer parallel programs

Morita, Kazutaka; Morihata, Akimasa; Matsuzaki, Kiminori; Hu, Zhenjiang; Takeichi, Masato

doi:10.1145/1250734.1250752

Cited by 50 publications

(32 citation statements)

References 21 publications

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“…Our motivation was to derive "the third homomorphism theorem" on trees. The theorem, which was first introduced by Gibbons (1996), is useful for developing parallel programs, and automatic parallelization methods have been proposed (Geser and Gorlatch 1999;Morita et al 2007) based on the theorem. Our theorem is an exact generalization of the original third homomorphism theorem, and our results are built on list homomorphisms.…”

Section: Discussionmentioning

confidence: 99%

“…Right inverses, which are generalizations of inverse functions, are useful for developing divide-and-conquer parallel programs (Gibbons 1996; Morita et al 2007). …”

Section: Right Inversesmentioning

confidence: 99%

“…Lemma 2.4 (Gibbons (1996); Morita et al (2007)). Assume that the following equations hold for function h.…”

Section: List Homomorphisms and The Third Homomorphism Theoremmentioning

confidence: 99%

“…In other words, two sequential programs lead to a scalable divide-andconquer parallel program. The third homomorphism theorem is useful for developing parallel programs, and automatic parallelization methods have been proposed based on the theorem (Geser and Gorlatch 1999;Morita et al 2007).…”

Section: Introductionmentioning

confidence: 99%

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The third homomorphism theorem on trees

Morihata

Matsuzaki

et al. 2009

Proceedings of the 36th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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Parallel programs on lists have been intensively studied. It is well known that associativity provides a good characterization for divide-and-conquer parallel programs. In particular, the third homomorphism theorem is not only useful for systematic development of parallel programs on lists, but it is also suitable for automatic parallelization. The theorem states that if two sequential programs iterate the same list leftward and rightward, respectively, and compute the same value, then there exists a divide-and-conquer parallel program that computes the same value as the sequential programs.While there have been many studies on lists, few have been done for characterizing and developing of parallel programs on trees. Naive divide-and-conquer programs, which divide a tree at the root and compute independent subtrees in parallel, take time that is proportional to the height of the input tree and have poor scalability with respect to the number of processors when the input tree is ill-balanced.In this paper, we develop a method for systematically constructing scalable divide-and-conquer parallel programs on trees, in which two sequential programs lead to a scalable divide-andconquer parallel program. We focus on paths instead of trees so as to utilize rich results on lists and demonstrate that associativity provides good characterization for scalable divide-and-conquer parallel programs on trees. Moreover, we generalize the third homomorphism theorem from lists to trees. We demonstrate the effectiveness of our method with various examples. Our results, being generalizations of known results for lists, are generic in the sense that they work well for all polynomial data structures.

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Section: Discussionmentioning

confidence: 99%

“…Right inverses, which are generalizations of inverse functions, are useful for developing divide-and-conquer parallel programs (Gibbons 1996; Morita et al 2007). …”

Section: Right Inversesmentioning

confidence: 99%

“…Lemma 2.4 (Gibbons (1996); Morita et al (2007)). Assume that the following equations hold for function h.…”

Section: List Homomorphisms and The Third Homomorphism Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The third homomorphism theorem on trees

Morihata

Matsuzaki

et al. 2009

Proceedings of the 36th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

Self Cite

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“…As part of an approach to generate divide-and-conquer parallel functional programs, Morita et al show how to compute a weak right inverse to a program fragment [29]. It is unclear whether this approach can handle loops.…”

Section: Related Workmentioning

confidence: 99%

Path-based inductive synthesis for program inversion

et al. 2011

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In this paper, we investigate the problem of semi-automated inversion of imperative programs, which has the potential to make it much easier and less error prone to write programs that naturally pair as inverses, such as insert/delete operations, compressors/decompressors, and so on. Viewing inversion as a subproblem of program synthesis, we propose a novel synthesis technique called Path-based Inductive Synthesis (PINS) and apply it to inversion. PINS starts from a program P and a template T for its inverse. PINS then iteratively refines the space of template instantiations by exploring paths in the composition of P and T with symbolic execution. PINS uses an SMT solver to intelligently guide the refinement process, based on the paths explored so far. The key idea motivating this approach is the small path-bound hypothesis: that the behavior of a program can be summarized with a small, carefully chosen set of its program paths.We evaluated PINS by using it to invert 14 programs such as compressors (e.g., Lempel-Ziv-Welch), encoders (e.g., UUEncode), and arithmetic operations (e.g., vector rotation). Most of these examples are difficult or impossible to invert using prior techniques, but PINS was able to invert all of them. We also found that a semi-automated technique we developed to mine a template from the program to be inverted worked well. In our experiments, PINS takes between one second to thirty minutes to synthesize inverses. We believe this proof-of-concept implementation demonstrates the viability of the PINS approach to program synthesis.

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Incremental Computing with Abstract Data Structures

Morihata

2016

Lecture Notes in Computer Science

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Automatic inversion generates divide-and-conquer parallel programs

Cited by 50 publications

References 21 publications

The third homomorphism theorem on trees

The third homomorphism theorem on trees

Path-based inductive synthesis for program inversion

Incremental Computing with Abstract Data Structures

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