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dc.contributor.authorReps, Thomas
dc.contributor.authorTuretsky, Emma
dc.contributor.authorPrabhu, Prathmesh
dc.description.abstractRecently, 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 ``c*X + X*d'' 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: ``c*X + X*d'' 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.en
dc.subjecttensor producten
dc.subjectregular expressionen
dc.subjectinterprocedural program analysisen
dc.subjectpolynomial fixed-point equationen
dc.subjectNewton's methoden
dc.titleNewtonian Program Analysis via Tensor Producten
dc.typeTechnical Reporten

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    Technical Reports Archive for the Department of Computer Sciences at the University of Wisconsin-Madison

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