Paper Info
Title
TIGHT POLYNOMIAL WORST-CASE BOUNDS FOR LOOP PROGRAMS
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.
Year
DOI
Venue
2019
10.23638/LMCS-16(2:4)2020
LOGICAL METHODS IN COMPUTER SCIENCE
Keywords
DocType
Volume
asymptotically-tight,multivariate,disjunctive,worst-case,polynomial bounds
Journal
16
Issue
ISSN
Citations 
2
1860-5974
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Amir M Ben-Amram132730.52
G. W. Hamilton2526.64