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Tight polynomial worst-case bounds for loop programs

Ben-Amram, Amir M. and Hamilton, Geoff orcid logoORCID: 0000-0001-5954-6444 (2020) Tight polynomial worst-case bounds for loop programs. Logical Methods in Computer Science, 16 (2). 4:1-4:39. ISSN 1860-5974

Abstract
In 2008, Ben-Amram, Jones and Kristiansen showed that for a simple programming language - representing non-deterministic imperative programs with bounded loops, and arithmetics limited to addition and multiplication - it is possible to decide precisely whether a program has certain growth-rate properties, in particular whether a computed value, or the program's running time, has a polynomial growth rate. A natural and intriguing problem was to move from answering the decision problem to giving a quantitative result, namely, a tight polynomial upper bound. This paper shows how to obtain asymptotically-tight, multivariate, disjunctive polynomial bounds for this class of programs. This is a complete solution: whenever a polynomial bound exists it will be found. A pleasant surprise is that the algorithm is quite simple; but it relies on some subtle reasoning. An important ingredient in the proof is the forest factorization theorem, a strong structural result on homomorphisms into a finite monoid.
Metadata
Item Type:Article (Published)
Refereed:Yes
Additional Information:First published 5 Apr 2019 in International Conference on Foundations of Software Science and Computation Structures FoSSaCS 2019: Foundations of Software Science and Computation Structures pp 80-97 as part of Lecture Notes in Computer Science, vol 11425. pp Springer, Cham. ISBN 978-3-030-17126-1 DOI: https://doi-org.dcu.idm.oclc.org/10.1007/978-3-030-17127-8_5
Uncontrolled Keywords:Computer Science; Logic in Computer Science
Subjects:Computer Science > Computational complexity
DCU Faculties and Centres:DCU Faculties and Schools > Faculty of Engineering and Computing > School of Computing
Publisher:Logical Methods in Computer Science
Official URL:https://lmcs.episciences.org/6477
Copyright Information:© 2020 The Authors
Use License:This item is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 3.0 License. View License
ID Code:24460
Deposited On:15 May 2020 11:04 by Vidatum Academic . Last Modified 15 May 2020 11:04
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