Time-complexity semantics for feasible affine recursions (extended abstract)

Details Time-complexity semantics for feasible affine recursions (extended abstract) Time-complexity semantics for feasible affine recursions (extended abstract)

2007-01-11

arxiv.org/abs/cs/0701076v2

Computer Science

Logic in Computer Science

Typographical fixes; some rearrangement of material. A shortened version is to appear in S.B. Cooper, B. Lowe, A. Sorbi (eds.)

Scientific paper

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.

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