Switch to: References

Add citations

You must login to add citations.
  1. The Equivalence of Definitions of Algorithmic Randomness.Christopher Porter - 2021 - Philosophia Mathematica 29 (2):153–194.
    In this paper, I evaluate the claim that the equivalence of multiple intensionally distinct definitions of random sequence provides evidence for the claim that these definitions capture the intuitive conception of randomness, concluding that the former claim is false. I then develop an alternative account of the significance of randomness-theoretic equivalence results, arguing that they are instances of a phenomenon I refer to as schematic equivalence. On my account, this alternative approach has the virtue of providing the plurality of definitions (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  • The K -Degrees, Low for K Degrees,and Weakly Low for K Sets.Joseph S. Miller - 2009 - Notre Dame Journal of Formal Logic 50 (4):381-391.
    We call A weakly low for K if there is a c such that $K^A(\sigma)\geq K(\sigma)-c$ for infinitely many σ; in other words, there are infinitely many strings that A does not help compress. We prove that A is weakly low for K if and only if Chaitin's Ω is A-random. This has consequences in the K-degrees and the low for K (i.e., low for random) degrees. Furthermore, we prove that the initial segment prefix-free complexity of 2-random reals is infinitely (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  • On Reals with -Bounded Complexity and Compressive Power.Ian Herbert - 2016 - Journal of Symbolic Logic 81 (3):833-855.
    The Kolmogorov complexity of a finite binary string is the length of the shortest description of the string. This gives rise to some ‘standard’ lowness notions for reals: A isK-trivial if its initial segments have the lowest possible complexity and A is low forKif using A as an oracle does not decrease the complexity of strings by more than a constant factor. We weaken these notions by requiring the defining inequalities to hold only up to all${\rm{\Delta }}_2^0$orders, and call the (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  • Calibrating Randomness.Rod Downey, Denis R. Hirschfeldt, André Nies & Sebastiaan A. Terwijn - 2006 - Bulletin of Symbolic Logic 12 (3):411-491.
    We report on some recent work centered on attempts to understand when one set is more random than another. We look at various methods of calibration by initial segment complexity, such as those introduced by Solovay [125], Downey, Hirschfeldt, and Nies [39], Downey, Hirschfeldt, and LaForte [36], and Downey [31]; as well as other methods such as lowness notions of Kučera and Terwijn [71], Terwijn and Zambella [133], Nies [101, 100], and Downey, Griffiths, and Reid [34]; higher level randomness notions (...)
    Direct download (11 more)  
     
    Export citation  
     
    Bookmark   28 citations  
  • Algorithmic Randomness and Measures of Complexity.George Barmpalias - 2013 - Bulletin of Symbolic Logic 19 (3):318-350.
  • Algorithmic Randomness and Measures of Complexity.George Barmpalias - 2013 - Bulletin of Symbolic Logic 19 (3):318-350.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation