Recently, Esparza et al. generalized Newton’s method – a numerical-analysis algorithm for finding roots of real-valued functions – to a method for finding fixed-points of systems of equations over semirings. Their method provides a new way to solve interprocedural dataflow-analysis problems. As in its real-valued counterpart, each iteration of their method solves a simpler ``linearized'' problem.
One of the reasons this advance is exciting is that some numerical analysts have claimed that "all effective and fast iterative [numerical] methods are forms (perhaps very disguised) of Newton’s method.'' However, there is an important difference between the dataflow-analysis and numerical-analysis contexts: when Newton’s method is used on numerical-analysis problems, multiplicative commutativity is relied on to rearrange expressions of the form “cX + Xd” into “(c+d) * X.” Such equations correspond to path problems described by regular languages. In contrast, when Newton’s method is used for interprocedural dataflow analysis, the ``multiplication'' operation involves function composition, and hence is non-commutative: “cX + Xd” cannot be rearranged into “(c+d) * X.” Such equations correspond to path problems described by linear context-free languages (LCFLs).
In this paper, we present an improved technique for solving the LCFL sub-problems produced during successive rounds of Newton’s method. Our method applies to predicate abstraction, on which most of today’s software model checkers rely.
Fri 22 JanDisplayed time zone: Guadalajara, Mexico City, Monterrey change
10:30 - 12:10
|Newtonian Program Analysis via Tensor Product|
Thomas Reps University of Wisconsin - Madison and Grammatech Inc., Emma Turetsky CS Dept., Univ. of Wisconsin-Madison, Prathmesh Prabhu GoogleMedia Attached
|Casper: An Efficient Approach to Call Trace Collection|
Rongxin Wu Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Xiao Xiao The Hong Kong University of Science and Technology, Shing-Chi Cheung Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Hongyu Zhang Microsoft Research, Charles Zhang HKUSTMedia Attached
|Pushdown Control-flow Analysis for Free|
Thomas Gilray University of Utah, Steven Lyde , Michael D. Adams University of Utah, Matthew Might University of Utah, USA, David Van Horn University of Maryland, College ParkPre-print Media Attached
|Binding as Sets of Scopes|
Matthew Flatt University of UtahPre-print Media Attached