article

Optimizing Ackermann's function by incrementalization

Authors:

Yanhong A. Liu,

Scott D. StollerAuthors Info & Claims

ACM SIGPLAN Notices, Volume 38, Issue 10

Pages 85 - 91

https://doi.org/10.1145/966049.777398

Published: 07 June 2003 Publication History

Abstract

This paper describes a formal derivation of an optimized Ackermann's function following a general and systematic method based on incrementalization. The method identifies an appropriate input increment operation and computes the function by repeatedly performing an incremental computation at the step of the increment. This eliminates repeated subcomputations in executions that follow the straightforward recursive definition of Ackermann's function, yielding an optimized program that is drastically faster and takes extremely little space. This case study uniquely shows the power and limitation of the incrementalization method, as well as both the iterative and recursive nature of computation underlying the optimized Ackermann's function.

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Cited By

Li FKlette R(2011)Approximate Shortest Paths in Simple PolyhedraDiscrete Geometry for Computer Imagery10.1007/978-3-642-19867-0_43(513-524)Online publication date: 2011
https://doi.org/10.1007/978-3-642-19867-0_43
Li FKlette R(2011)Approximate shortest paths in simple polyhedraProceedings of the 16th IAPR international conference on Discrete geometry for computer imagery10.5555/1987119.1987170(513-524)Online publication date: 6-Apr-2011
https://dl.acm.org/doi/10.5555/1987119.1987170

Index Terms

Optimizing Ackermann's function by incrementalization
1. Software and its engineering
  1. Software notations and tools
    1. Compilers
    2. General programming languages
      1. Language features
        Control structures
        Recursion
2. Theory of computation
  1. Semantics and reasoning
    1. Program semantics

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This paper describes a formal derivation of an optimized Ackermann's function following a general and systematic method based on incrementalization. The method identifies an appropriate input increment operation and computes the function by repeatedly ...
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Published In

cover image ACM SIGPLAN Notices

ACM SIGPLAN Notices Volume 38, Issue 10

Proceedings of the ACM SIGPLAN symposium on principles and practice of parallel programming (PPoPP 2003) and workshop on partial evaluation and semantics-based program manipulation (PEPM 2003)

October 2003

331 pages

ISSN:0362-1340

EISSN:1558-1160

DOI:10.1145/966049

Issue’s Table of Contents

PEPM '03: Proceedings of the 2003 ACM SIGPLAN workshop on Partial evaluation and semantics-based program manipulation
June 2003
100 pages
ISBN:1581136676
DOI:10.1145/777388
Program Chair:
Michael Leuschel
University of Southampton, UK

Copyright © 2003 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 07 June 2003

Published in SIGPLAN Volume 38, Issue 10

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Cited By

Li FKlette R(2011)Approximate Shortest Paths in Simple PolyhedraDiscrete Geometry for Computer Imagery10.1007/978-3-642-19867-0_43(513-524)Online publication date: 2011
https://doi.org/10.1007/978-3-642-19867-0_43
Li FKlette R(2011)Approximate shortest paths in simple polyhedraProceedings of the 16th IAPR international conference on Discrete geometry for computer imagery10.5555/1987119.1987170(513-524)Online publication date: 6-Apr-2011
https://dl.acm.org/doi/10.5555/1987119.1987170

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