Time-complexity semantics for feasible affine recursions (extended abstract)
<|reference_start|>Time-complexity semantics for feasible affine recursions (extended 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.<|reference_end|>
@article{danner2007time-complexity,
    title={Time-complexity semantics for feasible affine recursions (extended
  abstract)},
    author={Norman Danner and James S. Royer},
    journal={arXiv preprint arXiv:cs/0701076},
    year={2007},
    archivePrefix={arXiv},
    eprint={cs/0701076},
    primaryClass={cs.LO}
}