research-article

Multivariate amortized resource analysis

Authors:

Martin HofmannAuthors Info & Claims

POPL '11: Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages

Pages 357 - 370

https://doi.org/10.1145/1926385.1926427

Published: 26 January 2011 Publication History

Abstract

We study the problem of automatically analyzing the worst-case resource usage of procedures with several arguments. Existing automatic analyses based on amortization, or sized types bound the resource usage or result size of such a procedure by a sum of unary functions of the sizes of the arguments.

In this paper we generalize this to arbitrary multivariate polynomial functions thus allowing bounds of the form mn which had to be grossly overestimated by m²+n² before. Our framework even encompasses bounds like ∗_i,j≤n m_i m_j where the m_i are the sizes of the entries of a list of length n.

This allows us for the first time to derive useful resource bounds for operations on matrices that are represented as lists of lists and to considerably improve bounds on other super-linear operations on lists such as longest common subsequence and removal of duplicates from lists of lists.

Furthermore, resource bounds are now closed under composition which improves accuracy of the analysis of composed programs when some or all of the components exhibit super-linear resource or size behavior.

The analysis is based on a novel multivariate amortized resource analysis. We present it in form of a type system for a simple first-order functional language with lists and trees, prove soundness, and describe automatic type inference based on linear programming.

We have experimentally validated the automatic analysis on a wide range of examples from functional programming with lists and trees. The obtained bounds were compared with actual resource consumption. All bounds were asymptotically tight, and the constants were close or even identical to the optimal ones.

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Cited By

Pham LSaad FHoffmann J(2024)Robust Resource Bounds with Static Analysis and Bayesian InferenceProceedings of the ACM on Programming Languages10.1145/36563808:PLDI(76-101)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656380
Chen CZhang ZTian HYan SXu HChandra SBlincoe KTonella P(2023)OOM-Guard: Towards Improving the Ergonomics of Rust OOM Handling via a Reservation-Based ApproachProceedings of the 31st ACM Joint European Software Engineering Conference and Symposium on the Foundations of Software Engineering10.1145/3611643.3616303(733-744)Online publication date: 30-Nov-2023
https://dl.acm.org/doi/10.1145/3611643.3616303
Lorenzen ALeijen DSwierstra W(2023)FP²: Fully in-Place Functional ProgrammingProceedings of the ACM on Programming Languages10.1145/36078407:ICFP(275-304)Online publication date: 31-Aug-2023
https://dl.acm.org/doi/10.1145/3607840
Show More Cited By

Index Terms

Multivariate amortized resource analysis
1. Theory of computation
  1. Logic
  2. Semantics and reasoning
    1. Program reasoning
      1. Program analysis
    2. Program semantics

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We study the problem of automatically analyzing the worst-case resource usage of procedures with several arguments. Existing automatic analyses based on amortization, or sized types bound the resource usage or result size of such a procedure by a sum of ...

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cover image ACM Conferences

POPL '11: Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages

January 2011

652 pages

ISBN:9781450304900

DOI:10.1145/1926385

General Chair:
Thomas Ball
Microsoft Research, USA
,
Program Chair:
Mooly Sagiv
Tel Aviv University, Israel

ACM SIGPLAN Notices Volume 46, Issue 1
POPL '11
January 2011
624 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/1925844
Issue’s Table of Contents

Copyright © 2011 ACM.

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Published: 26 January 2011

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POPL '11: The 38th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

January 26 - 28, 2011

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Cited By

Pham LSaad FHoffmann J(2024)Robust Resource Bounds with Static Analysis and Bayesian InferenceProceedings of the ACM on Programming Languages10.1145/36563808:PLDI(76-101)Online publication date: 20-Jun-2024
https://dl.acm.org/doi/10.1145/3656380
Chen CZhang ZTian HYan SXu HChandra SBlincoe KTonella P(2023)OOM-Guard: Towards Improving the Ergonomics of Rust OOM Handling via a Reservation-Based ApproachProceedings of the 31st ACM Joint European Software Engineering Conference and Symposium on the Foundations of Software Engineering10.1145/3611643.3616303(733-744)Online publication date: 30-Nov-2023
https://dl.acm.org/doi/10.1145/3611643.3616303
Lorenzen ALeijen DSwierstra W(2023)FP²: Fully in-Place Functional ProgrammingProceedings of the ACM on Programming Languages10.1145/36078407:ICFP(275-304)Online publication date: 31-Aug-2023
https://dl.acm.org/doi/10.1145/3607840
Shaikhha AKelepeshis MGhorbani MDubach CBruening DHardekopf B(2023)Fine-Tuning Data Structures for Query ProcessingProceedings of the 21st ACM/IEEE International Symposium on Code Generation and Optimization10.1145/3579990.3580016(149-161)Online publication date: 17-Feb-2023
https://dl.acm.org/doi/10.1145/3579990.3580016
Grosen JKahn DHoffmann J(2023)Automatic Amortized Resource Analysis with Regular Recursive Types2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS56636.2023.10175720(1-14)Online publication date: 26-Jun-2023
https://doi.org/10.1109/LICS56636.2023.10175720
Gurdeep Singh RScholliers C(2023)GaiwanScience of Computer Programming10.1016/j.scico.2023.102989230:COnline publication date: 1-Aug-2023
https://dl.acm.org/doi/10.1016/j.scico.2023.102989
Žikelić ĐChang BBolignano PRaimondi FJhala RDillig I(2022)Differential cost analysis with simultaneous potentials and anti-potentialsProceedings of the 43rd ACM SIGPLAN International Conference on Programming Language Design and Implementation10.1145/3519939.3523435(442-457)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519939.3523435
Hoffmann JJost S(2022)Two decades of automatic amortized resource analysisMathematical Structures in Computer Science10.1017/S096012952100048732:6(729-759)Online publication date: 16-Mar-2022
https://doi.org/10.1017/S0960129521000487
Rajani VGaboardi MGarg DHoffmann J(2021)A unifying type-theory for higher-order (amortized) cost analysisProceedings of the ACM on Programming Languages10.1145/34343085:POPL(1-28)Online publication date: 4-Jan-2021
https://dl.acm.org/doi/10.1145/3434308
Barthe GBlazy SHutin RPichardie D(2021)Secure Compilation of Constant-Resource Programs2021 IEEE 34th Computer Security Foundations Symposium (CSF)10.1109/CSF51468.2021.00020(1-12)Online publication date: Jun-2021
https://doi.org/10.1109/CSF51468.2021.00020
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