NDLI: Newtonian program analysis

Content Provider	ACM Digital Library
Author	Esparza, Javier Kiefer, Stefan Luttenberger, Michael
Copyright Year	2010
Abstract	This article presents a novel generic technique for solving dataflow equations in interprocedural dataflow analysis. The technique is obtained by generalizing Newton's method for computing a zero of a differentiable function to ω-continuous semirings. Complete semilattices, the common program analysis framework, are a special class of ω-continuous semirings. We show that our generalized method always converges to the solution, and requires at most as many iterations as current methods based on Kleene's fixed-point theorem. We also show that, contrary to Kleene's method, Newton's method always terminates for arbitrary idempotent and commutative semirings. More precisely, in the latter setting the number of iterations required to solve a system of $\textit{n}$ equations is at most $\textit{n}.$
Starting Page	1
Ending Page	47
Page Count	47
File Format	PDF
ISSN	00045411
e-ISSN	1557735X
DOI	10.1145/1857914.1857917
Journal	Journal of the ACM (JACM)
Volume Number	57
Issue Number	6
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2010-11-05
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Newton's method Interprocedural program analysis Polynomial fixed-point equations Semirings
Content Type	Text
Resource Type	Article
Subject	Hardware and Architecture Information Systems Control and Systems Engineering Artificial Intelligence Software

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