Cover's test of rationality revisited: Computability aspects of hypothesis testing

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    1 Scopus citations

    Abstract

    In this paper we discuss computability aspects of hypothesis testing. We describe two main results. First we determine the type of sets that admit a weak decision procedure. Surprisingly some non-computable sets admit a computable weak decision procedure. This strengthens results of Cover and Putnam. We then apply the notion of weak decision procedure to the testing of the physical Church-Turing thesis. While our first theorem states that there are non-computable sets that admit weak decision procedures, we are able to show that no weak decision procedure can help us to decide that a physical device is capable of computing non Turing computable functions or that a physical constant encodes the bits of a non-computable real. This has strong implications on the validity of physical theories entailing the failure of the physical Church-Turing thesis.

    Original languageEnglish
    Title of host publication2006 IEEE 24th Convention of Electrical and Electronics Engineers in Israel, IEEEI
    Pages213-216
    Number of pages4
    DOIs
    StatePublished - 2006
    Event2006 IEEE 24th Convention of Electrical and Electronics Engineers in Israel, IEEEI - Eilat, Israel
    Duration: 15 Nov 200617 Nov 2006

    Publication series

    NameIEEE Convention of Electrical and Electronics Engineers in Israel, Proceedings

    Conference

    Conference2006 IEEE 24th Convention of Electrical and Electronics Engineers in Israel, IEEEI
    Country/TerritoryIsrael
    CityEilat
    Period15/11/0617/11/06

    Fingerprint

    Dive into the research topics of 'Cover's test of rationality revisited: Computability aspects of hypothesis testing'. Together they form a unique fingerprint.

    Cite this