Polynomial running times for polynomial-Time oracle machines

Akitoshi Kawamura, Florian Steinberg

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

This paper introduces a more restrictive notion of feasibility of functionals on Baire space than the established one from second-order complexity theory. Thereby making it possible to consider functions on the natural numbers as running times of oracle Turing machines and avoiding secondorder polynomials, which are notoriously difficult to handle. Furthermore, all machines that witness this stronger kind of feasibility can be clocked and the different traditions of treating partial functionals from computable analysis and second-order complexity theory are equated in a precise sense. The new notion is named 'strong polynomial-Time computability', and proven to be a strictly stronger requirement than polynomial-Time computability. It is proven that within the framework for complexity of operators from analysis introduced by Kawamura and Cook the classes of strongly polynomial-Time computable functionals and polynomial-Time computable functionals coincide.

Original languageEnglish
Title of host publication2nd International Conference on Formal Structures for Computation and Deduction, FSCD 2017
EditorsDale Miller
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770477
DOIs
Publication statusPublished - Sep 1 2017
Externally publishedYes
Event2nd International Conference on Formal Structures for Computation and Deduction, FSCD 2017 - Oxford, United Kingdom
Duration: Sep 3 2017Sep 9 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume84
ISSN (Print)1868-8969

Other

Other2nd International Conference on Formal Structures for Computation and Deduction, FSCD 2017
CountryUnited Kingdom
CityOxford
Period9/3/179/9/17

All Science Journal Classification (ASJC) codes

  • Software

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