Flow Analysis, Linearity, and PTIME

TitleFlow Analysis, Linearity, and PTIME
Publication TypeBook Chapters
Year of Publication2008
AuthorsVan Horn D, Mairson HG
EditorAlpuente M, Vidal G
Book TitleStatic Analysis
Series TitleLecture Notes in Computer Science
Pagination255 - 269
PublisherSpringer Berlin Heidelberg
ISBN Number978-3-540-69163-1, 978-3-540-69166-2
KeywordsLogics and Meanings of Programs, Mathematical Logic and Formal Languages, Programming Languages, Compilers, Interpreters, Programming Techniques, software engineering

Flow analysis is a ubiquitous and much-studied component of compiler technology—and its variations abound. Amongst the most well known is Shivers’ 0CFA; however, the best known algorithm for 0CFA requires time cubic in the size of the analyzed program and is unlikely to be improved. Consequently, several analyses have been designed to approximate 0CFA by trading precision for faster computation. Henglein’s simple closure analysis, for example, forfeits the notion of directionality in flows and enjoys an “almost linear” time algorithm. But in making trade-offs between precision and complexity, what has been given up and what has been gained? Where do these analyses differ and where do they coincide? We identify a core language—the linear λ-calculus—where 0CFA, simple closure analysis, and many other known approximations or restrictions to 0CFA are rendered identical. Moreover, for this core language, analysis corresponds with (instrumented) evaluation. Because analysis faithfully captures evaluation, and because the linear λ-calculus is complete for ptime, we derive ptime-completeness results for all of these analyses.