# Type-two Iteration with Bounded Query Revision

@inproceedings{Kapron2019TypetwoIW, title={Type-two Iteration with Bounded Query Revision}, author={Bruce M. Kapron and Florian Steinberg}, booktitle={DICE-FOPARA@ETAPS}, year={2019} }

Motivated by recent results of Kapron and Steinberg (LICS 2018) we introduce new forms of iteration on length in the setting of applied lambda-calculi for higher-type poly-time computability. In particular, in a type-two setting, we consider functionals which capture iteration on input length which bound interaction with the type-one input parameter, by restricting to a constant either the number of times the function parameter may return a value of increasing size, or the number of times the…

## 3 Citations

### Type-two polynomial-time and restricted lookahead

- Computer Science, MathematicsLICS
- 2018

This paper provides an alternate characterization of second-order polynomial-time computability, by refining the notion of oracle-poly- time computability introduced by Cook, and proves that all feasible problems can be solved within this class if one is allowed to separate a task into efficiently solvable subtasks.

### Complete and tractable machine-independent characterizations of second-order polytime

- Computer ScienceFoSSaCS
- 2022

As typing is decidable in polynomial time, this work obtains the first tractable, sound, complete, and implicit characterization of BFF, thus solving a problem opened for more than 20 years.

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- Computer ScienceLICS
- 2020

A characterization of BFF2 is given based on an imperative language with oracle calls using a tier-based type system whose inference is decidable, which should make it possible to link higher-order complexity with programming theory.

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