---
res:
bibo_abstract:
- "We study the problem of developing efficient approaches for proving\r\nworst-case
bounds of non-deterministic recursive programs. Ranking functions\r\nare sound
and complete for proving termination and worst-case bounds of\r\nnonrecursive
programs. First, we apply ranking functions to recursion,\r\nresulting in measure
functions. We show that measure functions provide a sound\r\nand complete approach
to prove worst-case bounds of non-deterministic recursive\r\nprograms. Our second
contribution is the synthesis of measure functions in\r\nnonpolynomial forms.
We show that non-polynomial measure functions with\r\nlogarithm and exponentiation
can be synthesized through abstraction of\r\nlogarithmic or exponentiation terms,
Farkas' Lemma, and Handelman's Theorem\r\nusing linear programming. While previous
methods obtain worst-case polynomial\r\nbounds, our approach can synthesize bounds
of the form $\\mathcal{O}(n\\log n)$\r\nas well as $\\mathcal{O}(n^r)$ where $r$
is not an integer. We present\r\nexperimental results to demonstrate that our
approach can obtain efficiently\r\nworst-case bounds of classical recursive algorithms
such as (i) Merge-Sort, the\r\ndivide-and-conquer algorithm for the Closest-Pair
problem, where we obtain\r\n$\\mathcal{O}(n \\log n)$ worst-case bound, and (ii)
Karatsuba's algorithm for\r\npolynomial multiplication and Strassen's algorithm
for matrix multiplication,\r\nwhere we obtain $\\mathcal{O}(n^r)$ bound such that
$r$ is not an integer and\r\nclose to the best-known bounds for the respective
algorithms.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Krishnendu
foaf_name: Chatterjee, Krishnendu
foaf_surname: Chatterjee
foaf_workInfoHomepage: http://www.librecat.org/personId=2E5DCA20-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-4561-241X
- foaf_Person:
foaf_givenName: Hongfei
foaf_name: Fu, Hongfei
foaf_surname: Fu
- foaf_Person:
foaf_givenName: Amir Kafshdar
foaf_name: Goharshady, Amir Kafshdar
foaf_surname: Goharshady
foaf_workInfoHomepage: http://www.librecat.org/personId=391365CE-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0003-1702-6584
bibo_doi: 10.1145/3339984
bibo_issue: '4'
bibo_volume: 41
dct_date: 2019^xs_gYear
dct_language: eng
dct_publisher: ACM@
dct_title: Non-polynomial worst-case analysis of recursive programs@
...