Time-Complexity Semantics for Feasible Affine Recursions

Authors:
Norman Danner;James S. Royer
Affiliations:
Department of Mathematics and Computer Science, Wesleyan University, Middletown, CT 06459, USA;Department of Electrical Engineering and Computer Science, Syracuse University, Syracuse, NY 13210, USA
Venue:
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Year:
2007

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Abstract

The authors' ATRprogramming formalism is a version of call-by-value PCFunder a complexity-theoretically motivated type system. ATRprograms run in type-2 polynomial-time and all standard type-2 basic feasible functionals are ATR-definable (ATRtypes are confined to levels 0, 1, and 2). A limitation of the original version of ATRis that the only directly expressible recursions are tail-recursions. Here we extend ATRso that a broad range of affine recursions are directly expressible. In particular, the revised ATRcan 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 ATRto develop a set of tools for extracting and solving the higher-type recurrences arising from feasible affine recursions.