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Time-Complexity Semantics for Feasible Affine Recursions

  • Norman Danner
  • James S. Royer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4497)

Abstract

The authors’ ATR programming formalism is a version of call-by-value PCF under a complexity-theoretically motivated type system. ATR programs run in type-2 polynomial-time and all standard type-2 basic feasible functionals are ATR-definable (ATR types are confined to levels 0, 1, and 2). A limitation of the original version of ATR is that the only directly expressible recursions are tail-recursions. Here we extend ATR so that a broad range of affine recursions are directly expressible. In particular, the revised ATR can fairly naturally express the classic insertion- and selection-sort algorithms, thus overcoming a sticking point of most prior implicit-complexity-based formalisms. The paper’s main work is in extending and simplifying the original time-complexity semantics for ATR to develop a set of tools for extracting and solving the higher-type recurrences arising from feasible affine recursions.

Keywords

Base Type Recursive Call Typing Rule Elimination Rule Type Context 
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 2007

Authors and Affiliations

  • Norman Danner
    • 1
  • James S. Royer
    • 2
  1. 1.Department of Mathematics and Computer Science, Wesleyan University, Middletown, CT 06459USA
  2. 2.Department of Electrical Engineering and Computer Science, Syracuse University, Syracuse, NY 13210USA

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