Flow Analysis, Linearity, and PTIME

  • David Van Horn
  • Harry G. Mairson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5079)


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.


Flow Analysis Turing Machine Linear Logic Type Inference Program Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • David Van Horn
    • 1
  • Harry G. Mairson
    • 1
  1. 1.Department of Computer ScienceBrandeis UniversityWaltham

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