TY - CHAP
T1 - Flow Analysis, Linearity, and PTIME
T2 - Static Analysis
Y1 - 2008
A1 - David Van Horn
A1 - Mairson, Harry G.
ED - Alpuente, María
ED - Vidal, Germán
KW - Logics and Meanings of Programs
KW - Mathematical Logic and Formal Languages
KW - Programming Languages, Compilers, Interpreters
KW - Programming Techniques
KW - software engineering
AB - 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.
JA - Static Analysis
T3 - Lecture Notes in Computer Science
PB - Springer Berlin Heidelberg
SN - 978-3-540-69163-1, 978-3-540-69166-2
UR - http://link.springer.com/chapter/10.1007/978-3-540-69166-2_17
ER -