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Inferring Lower Runtime Bounds for Integer Programs

Authors:

Marc Brockschmidt,

Jürgen GieslAuthors Info & Claims

ACM Transactions on Programming Languages and Systems (TOPLAS), Volume 42, Issue 3

Article No.: 13, Pages 1 - 50

https://doi.org/10.1145/3410331

Published: 15 October 2020 Publication History

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Abstract

We present a technique to infer lower bounds on the worst-case runtime complexity of integer programs, where in contrast to earlier work, our approach is not restricted to tail-recursion. Our technique constructs symbolic representations of program executions using a framework for iterative, under-approximating program simplification. The core of this simplification is a method for (under-approximating) program acceleration based on recurrence solving and a variation of ranking functions. Afterwards, we deduce asymptotic lower bounds from the resulting simplified programs using a special-purpose calculus and an SMT encoding. We implemented our technique in our tool LoAT and show that it infers non-trivial lower bounds for a large class of examples.

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Index Terms

Inferring Lower Runtime Bounds for Integer Programs
1. Software and its engineering
  1. Software organization and properties
    1. Extra-functional properties
      1. Software performance
2. Theory of computation

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Published In

cover image ACM Transactions on Programming Languages and Systems

ACM Transactions on Programming Languages and Systems Volume 42, Issue 3

September 2020

230 pages

ISSN:0164-0925

EISSN:1558-4593

DOI:10.1145/3430314

Editor:
Andrew Myers
Cornell University, USA

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Copyright © 2020 Owner/Author.

Permission to make digital or hard copies of part or all 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. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Association for Computing Machinery

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Publication History

Published: 15 October 2020

Accepted: 01 July 2020

Revised: 01 June 2020

Received: 01 September 2019

Published in TOPLAS Volume 42, Issue 3

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Cited By

Klinger AEhrmanntraut VMeyer UVilela JSchulmann HLi N(2024)Estimating the Runtime and Global Network Traffic of SMPC ProtocolsProceedings of the Fourteenth ACM Conference on Data and Application Security and Privacy10.1145/3626232.3653258(7-18)Online publication date: 19-Jun-2024
https://dl.acm.org/doi/10.1145/3626232.3653258
Frohn FGiesl J(2024)Integrating Loop Acceleration Into Bounded Model CheckingFormal Methods10.1007/978-3-031-71162-6_4(73-91)Online publication date: 11-Sep-2024
https://doi.org/10.1007/978-3-031-71162-6_4
Frohn FGiesl J(2024)Satisfiability Modulo Exponential Integer ArithmeticAutomated Reasoning10.1007/978-3-031-63498-7_21(344-365)Online publication date: 3-Jul-2024
https://dl.acm.org/doi/10.1007/978-3-031-63498-7_21
Feng SChen MSu HKaminski BKatoen JZhan N(2023)Lower Bounds for Possibly Divergent Probabilistic ProgramsProceedings of the ACM on Programming Languages10.1145/35860517:OOPSLA1(696-726)Online publication date: 6-Apr-2023
https://dl.acm.org/doi/10.1145/3586051
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
Frohn FFuhs C(2022)A calculus for modular loop acceleration and non-termination proofsInternational Journal on Software Tools for Technology Transfer (STTT)10.1007/s10009-022-00670-224:5(691-715)Online publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1007/s10009-022-00670-2
Lommen NMeyer FGiesl J(2022)Automatic Complexity Analysis of Integer Programs via Triangular Weakly Non-Linear LoopsAutomated Reasoning10.1007/978-3-031-10769-6_43(734-754)Online publication date: 8-Aug-2022
https://dl.acm.org/doi/10.1007/978-3-031-10769-6_43
Frohn FGiesl J(2022)Proving Non-Termination and Lower Runtime Bounds with LoAT (System Description)Automated Reasoning10.1007/978-3-031-10769-6_41(712-722)Online publication date: 8-Aug-2022
https://dl.acm.org/doi/10.1007/978-3-031-10769-6_41
Giesl JLommen NHark MMeyer F(2022)Improving Automatic Complexity Analysis of Integer ProgramsThe Logic of Software. A Tasting Menu of Formal Methods10.1007/978-3-031-08166-8_10(193-228)Online publication date: 4-Jul-2022
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Albert EGenaim SMartin-Martin EMerayo ARubio A(2021)Lower-Bound Synthesis Using Loop Specialization and Max-SMTComputer Aided Verification10.1007/978-3-030-81688-9_40(863-886)Online publication date: 20-Jul-2021
https://dl.acm.org/doi/10.1007/978-3-030-81688-9_40

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