Results for ' Schnorr randomness'

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  1.  25
    Schnorr Randomness.Rodney G. Downey & Evan J. Griffiths - 2004 - Journal of Symbolic Logic 69 (2):533 - 554.
    Schnorr randomness is a notion of algorithmic randomness for real numbers closely related to Martin-Löf randomness. After its initial development in the 1970s the notion received considerably less attention than Martin-Löf randomness, but recently interest has increased in a range of randomness concepts. In this article, we explore the properties of Schnorr random reals, and in particular the c.e. Schnorr random reals. We show that there are c.e. reals that are Schnorr (...)
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  2.  49
    Truth-table Schnorr randomness and truth-table reducible randomness.Kenshi Miyabe - 2011 - Mathematical Logic Quarterly 57 (3):323-338.
    Schnorr randomness and computable randomness are natural concepts of random sequences. However van Lambalgen’s Theorem fails for both randomnesses. In this paper we define truth-table Schnorr randomness and truth-table reducible randomness, for which we prove that van Lambalgen's Theorem holds. We also show that the classes of truth-table Schnorr random reals relative to a high set contain reals Turing equivalent to the high set. It follows that each high Schnorr random real is (...)
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  3. Evan," Schnorr randomness.Rodney& Griffiths Downey - 2004 - Journal of Symbolic Logic 69:2.
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  4.  27
    General random sequences and learnable sequences.C. P. Schnorr & P. Fuchs - 1977 - Journal of Symbolic Logic 42 (3):329-340.
    We formalise the notion of those infinite binary sequences z that admit a single program P which expresses the entire algorithmical structure of z. Such a program P minimizes the information which must be used in a relative computation for z. We propose two concepts with different strength for this notion, the learnable and the super-learnable sequences. We establish three different equivalent characterizations of learnable (super-learnable, resp.) sequences. In particular, we prove that a sequences z is learnable (super-learnable, resp.) if (...)
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  5.  4
    Kruse Arthur H.. Some notions of random sequence and their set-theoretic foundations. Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 13 , pp. 299–322. [REVIEW]C. P. Schnorr - 1973 - Journal of Symbolic Logic 38 (3):530-531.
  6.  3
    Lowness for the class of Schnorr random sets.B. Kjös-Hanssen, A. Nies & F. Stephan - 2005 - Notre Dame Journal of Formal Logic 35 (3):647-657.
    We answer a question of Ambos-Spies and Kuˇcera in the affirmative. They asked whether, when a real is low for Schnorr randomness, it is already low for Schnorr tests.
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  7.  39
    A learning-theoretic characterisation of Martin-Löf randomness and Schnorr randomness.Francesca Zaffora Blando - 2021 - Review of Symbolic Logic 14 (2):531-549.
    Numerous learning tasks can be described as the process of extrapolating patterns from observed data. One of the driving intuitions behind the theory of algorithmic randomness is that randomness amounts to the absence of any effectively detectable patterns: it is thus natural to regard randomness as antithetical to inductive learning. Osherson and Weinstein [11] draw upon the identification of randomness with unlearnability to introduce a learning-theoretic framework (in the spirit of formal learning theory) for modelling algorithmic (...)
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  8.  26
    On Schnorr and computable randomness, martingales, and machines.Rod Downey, Evan Griffiths & Geoffrey Laforte - 2004 - Mathematical Logic Quarterly 50 (6):613-627.
    We examine the randomness and triviality of reals using notions arising from martingales and prefix-free machines.
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  9.  60
    Reviewed Work(s): Lowness properties and randomness. Advances in Mathematics, vol. 197 by André Nies; Lowness for the class of Schnorr random reals. SIAM Journal on Computing, vol. 35 by Bjørn Kjos-Hanssen; André Nies; Frank Stephan; Lowness for Kurtz randomness. The Journal of Symbolic Logic, vol. 74 by Noam Greenberg; Joseph S. Miller; Randomness and lowness notions via open covers. Annals of Pure and Applied Logic, vol. 163 by Laurent Bienvenu; Joseph S. Miller; Relativizations of randomness and genericity notions. The Bulletin of the London Mathematical Society, vol. 43 by Johanna N. Y. Franklin; Frank Stephan; Liang Yu; Randomness notions and partial relativization. Israel Journal of Mathematics, vol. 191 by George Barmpalias; Joseph S. Miller; André Nies. [REVIEW]Johanna N. Y. Franklin - forthcoming - Association for Symbolic Logic: The Bulletin of Symbolic Logic.
    Review by: Johanna N. Y. Franklin The Bulletin of Symbolic Logic, Volume 19, Issue 1, Page 115-118, March 2013.
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  10.  21
    André Nies. Lowness properties and randomness. Advances in Mathematics, vol. 197 , no. 1, pp. 274–305. - Bjørn Kjos-Hanssen, André Nies, and Frank Stephan. Lowness for the class of Schnorr random reals. SIAM Journal on Computing, vol. 35 , no. 3, pp. 647–657. - Noam Greenberg and Joseph S. Miller. Lowness for Kurtz randomness. The Journal of Symbolic Logic, vol. 74 , no. 2, pp. 665–678. - Laurent Bienvenu and Joseph S. Miller. Randomness and lowness notions via open covers. Annals of Pure and Applied Logic, vol. 163 , no. 5, pp. 506–518. - Johanna N. Y. Franklin, Frank Stephan, and Liang. Yu Relativizations of randomness and genericity notions. The Bulletin of the London Mathematical Society, vol. 43 , no. 4, pp. 721–733. - George Barmpalias, Joseph S. Miller, and André Nies. Randomness notions and partial relativization. Israel Journal of Mathematics, vol. 191 , no. 2, pp. 791–816. [REVIEW]Johanna N. Y. Franklin - 2013 - Bulletin of Symbolic Logic 19 (1):115-118.
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  11.  8
    Schnorr trivial reals: a construction. [REVIEW]Johanna N. Y. Franklin - 2008 - Archive for Mathematical Logic 46 (7-8):665-678.
    A real is Martin-Löf (Schnorr) random if it does not belong to any effectively presented null ${\Sigma^0_1}$ (recursive) class of reals. Although these randomness notions are very closely related, the set of Turing degrees containing reals that are K-trivial has very different properties from the set of Turing degrees that are Schnorr trivial. Nies proved in (Adv Math 197(1):274–305, 2005) that all K-trivial reals are low. In this paper, we prove that if ${{\bf h'} \geq_T {\bf 0''}}$ (...)
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  12.  12
    Relativized Schnorr tests with universal behavior.Nicholas Rupprecht - 2010 - Archive for Mathematical Logic 49 (5):555-570.
    A Schnorr test relative to some oracle A may informally be called “universal” if it covers all Schnorr tests. Since no true universal Schnorr test exists, such an A cannot be computable. We prove that the sets with this property are exactly those with high Turing degree. Our method is closely related to the proof of Terwijn and Zambella’s characterization of the oracles which are low for Schnorr tests. We also consider the oracles which compute relativized (...)
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  13.  86
    Computational randomness and lowness.Sebastiaan A. Terwijn & Domenico Zambella - 2001 - Journal of Symbolic Logic 66 (3):1199-1205.
    We prove that there are uncountably many sets that are low for the class of Schnorr random reals. We give a purely recursion theoretic characterization of these sets and show that they all have Turing degree incomparable to 0'. This contrasts with a result of Kučera and Terwijn [5] on sets that are low for the class of Martin-Löf random reals.
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  14. Hyperimmune-free degrees and Schnorr triviality.Johanna N. Y. Franklin - 2008 - Journal of Symbolic Logic 73 (3):999-1008.
    We investigate the relationship between lowness for Schnorr randomness and Schnorr triviality. We show that a real is low for Schnorr randomness if and only if it is Schnorr trivial and hyperimmune free.
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  15. Subclasses of the Weakly Random Reals.Johanna N. Y. Franklin - 2010 - Notre Dame Journal of Formal Logic 51 (4):417-426.
    The weakly random reals contain not only the Schnorr random reals as a subclass but also the weakly 1-generic reals and therefore the n -generic reals for every n . While the class of Schnorr random reals does not overlap with any of these classes of generic reals, their degrees may. In this paper, we describe the extent to which this is possible for the Turing, weak truth-table, and truth-table degrees and then extend our analysis to the (...) random and hyperimmune reals. (shrink)
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  16.  15
    Randomness notions and reverse mathematics.André Nies & Paul Shafer - 2020 - Journal of Symbolic Logic 85 (1):271-299.
    We investigate the strength of a randomness notion ${\cal R}$ as a set-existence principle in second-order arithmetic: for each Z there is an X that is ${\cal R}$-random relative to Z. We show that the equivalence between 2-randomness and being infinitely often C-incompressible is provable in $RC{A_0}$. We verify that $RC{A_0}$ proves the basic implications among randomness notions: 2-random $\Rightarrow$ weakly 2-random $\Rightarrow$ Martin-Löf random $\Rightarrow$ computably random $\Rightarrow$ Schnorr random. Also, over $RC{A_0}$ the existence of (...)
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  17.  10
    Computable randomness and betting for computable probability spaces.Jason Rute - 2016 - Mathematical Logic Quarterly 62 (4-5):335-366.
    Unlike Martin‐Löf randomness and Schnorr randomness, computable randomness has not been defined, except for a few ad hoc cases, outside of Cantor space. This paper offers such a definition (actually, several equivalent definitions), and further, provides a general method for abstracting “bit‐wise” definitions of randomness from Cantor space to arbitrary computable probability spaces. This same method is also applied to give machine characterizations of computable and Schnorr randomness for computable probability spaces, extending the (...)
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  18.  75
    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 (...)
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  19.  37
    Lowness for Kurtz randomness.Noam Greenberg & Joseph S. Miller - 2009 - Journal of Symbolic Logic 74 (2):665-678.
    We prove that degrees that are low for Kurtz randomness cannot be diagonally non-recursive. Together with the work of Stephan and Yu [16], this proves that they coincide with the hyperimmune-free non-DNR degrees, which are also exactly the degrees that are low for weak 1-genericity. We also consider Low(M, Kurtz), the class of degrees a such that every element of M is a-Kurtz random. These are characterised when M is the class of Martin-Löf random, computably random, or Schnorr (...)
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  20.  27
    Uniform distribution and algorithmic randomness.Jeremy Avigad - 2013 - Journal of Symbolic Logic 78 (1):334-344.
    A seminal theorem due to Weyl [14] states that if $(a_n)$ is any sequence of distinct integers, then, for almost every $x \in \mathbb{R}$, the sequence $(a_n x)$ is uniformly distributed modulo one. In particular, for almost every $x$ in the unit interval, the sequence $(a_n x)$ is uniformly distributed modulo one for every computable sequence $(a_n)$ of distinct integers. Call such an $x$ UD random. Here it is shown that every Schnorr random real is UD random, but there (...)
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  21.  10
    Defining a randomness notion via another.Kojiro Higuchi & Ningning Peng - 2014 - Mathematical Logic Quarterly 60 (4-5):280-288.
    To compare two randomness notions with each other, we ask whether a given randomness notion can be defined via another randomness notion. Inspired by Yu's pioneering study, we formalize our question using the concept of relativization of randomness. We give some solutions to our formalized questions. Also, our results include the affirmative answer to the problem asked by Yu in a discussion with the second author, i.e., whether Schnorr randomness relative to the halting problem (...)
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  22. Every 2-random real is Kolmogorov random.Joseph S. Miller - 2004 - Journal of Symbolic Logic 69 (3):907-913.
    We study reals with infinitely many incompressible prefixes. Call $A \in 2^{\omega}$ Kolmogorot random if $(\exists^{\infty}n) C(A \upharpoonright n) \textgreater n - \mathcal{O}(1)$ , where C denotes plain Kolmogorov complexity. This property was suggested by Loveland and studied by $Martin-L\ddot{0}f$ , Schnorr and Solovay. We prove that 2-random reals are Kolmogorov random. Together with the converse-proved by Nies. Stephan and Terwijn [11]-this provides a natural characterization of 2-randomness in terms of plain complexity. We finish with a related characterization (...)
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  23.  6
    Martin-Löf Randomness Implies Multiple Recurrence in Effectively Closed Sets.Rodney G. Downey, Satyadev Nandakumar & André Nies - 2019 - Notre Dame Journal of Formal Logic 60 (3):491-502.
    This work contributes to the program of studying effective versions of “almost-everywhere” theorems in analysis and ergodic theory via algorithmic randomness. Consider the setting of Cantor space {0,1}N with the uniform measure and the usual shift. We determine the level of randomness needed for a point so that multiple recurrence in the sense of Furstenberg into effectively closed sets P of positive measure holds for iterations starting at the point. This means that for each k∈N there is an (...)
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  24.  42
    Probabilistic algorithmic randomness.Sam Buss & Mia Minnes - 2013 - Journal of Symbolic Logic 78 (2):579-601.
    We introduce martingales defined by probabilistic strategies, in which randomness is used to decide whether to bet. We show that different criteria for the success of computable probabilistic strategies can be used to characterize ML-randomness, computable randomness, and partial computable randomness. Our characterization of ML-randomness partially addresses a critique of Schnorr by formulating ML randomness in terms of a computable process rather than a computably enumerable function.
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  25.  10
    Russell's typicality as another randomness notion.Athanassios Tzouvaras - 2020 - Mathematical Logic Quarterly 66 (3):355-365.
    We reformulate slightly Russell's notion of typicality, so as to eliminate its circularity and make it applicable to elements of any first‐order structure. We argue that the notion parallels Martin‐Löf (ML) randomness, in the sense that it uses definable sets in place of computable ones and sets of “small” cardinality (i.e., strictly smaller than that of the structure domain) in place of measure zero sets. It is shown that if the domain M satisfies, then there exist typical elements and (...)
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  26. Van Lambalgen's Theorem and High Degrees.Johanna N. Y. Franklin & Frank Stephan - 2011 - Notre Dame Journal of Formal Logic 52 (2):173-185.
    We show that van Lambalgen's Theorem fails with respect to recursive randomness and Schnorr randomness for some real in every high degree and provide a full characterization of the Turing degrees for which van Lambalgen's Theorem can fail with respect to Kurtz randomness. However, we also show that there is a recursively random real that is not Martin-Löf random for which van Lambalgen's Theorem holds with respect to recursive randomness.
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  27.  22
    Constructive equivalence relations on computable probability measures.Laurent Bienvenu & Wolfgang Merkle - 2009 - Annals of Pure and Applied Logic 160 (3):238-254.
    A central object of study in the field of algorithmic randomness are notions of randomness for sequences, i.e., infinite sequences of zeros and ones. These notions are usually defined with respect to the uniform measure on the set of all sequences, but extend canonically to other computable probability measures. This way each notion of randomness induces an equivalence relation on the computable probability measures where two measures are equivalent if they have the same set of random sequences. (...)
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  28.  22
    Unified characterizations of lowness properties via Kolmogorov complexity.Takayuki Kihara & Kenshi Miyabe - 2015 - Archive for Mathematical Logic 54 (3-4):329-358.
    Consider a randomness notion C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}. A uniform test in the sense of C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document} is a total computable procedure that each oracle X produces a test relative to X in the sense of C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}. We say that a binary sequence Y is C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}-random uniformly relative (...)
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  29.  7
    Filosofias da diferença e a formação de professores: experimentações com ateliê de escrileituras.Samuel Molina Schnorr, Carla Gonçalves Rodrigues & Josimara Wikboldt Schwantz - 2017 - Educação E Filosofia 31 (61):369-384.
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  30.  15
    Level of risk in probability learning: Within- and between-subjects designs.John A. Schnorr, Stanley G. Lipkin & Jerome L. Myers - 1966 - Journal of Experimental Psychology 72 (4):497.
  31.  11
    Negative contrast in human probability learning as a function of incentive magnitudes.John A. Schnorr & Jerome L. Myers - 1967 - Journal of Experimental Psychology 75 (4):492.
  32.  18
    Arithmetical Measure.Sebastiaan A. Terwijn & Leen Torenvliet - 1998 - Mathematical Logic Quarterly 44 (2):277-286.
    We develop arithmetical measure theory along the lines of Lutz [10]. This yields the same notion of measure 0 set as considered before by Martin-Löf, Schnorr, and others. We prove that the class of sets constructible by r.e.-constructors, a direct analogue of the classes Lutz devised his resource bounded measures for in [10], is not equal to RE, the class of r.e. sets, and we locate this class exactly in terms of the common recursion-theoretic reducibilities below K. We note (...)
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  33.  9
    A characterization of complexity sequences.C. P. Schnorr & G. Stumpf - 1975 - Mathematical Logic Quarterly 21 (1):47-56.
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  34.  2
    Ateliês de Escrileituras.Samuel Molina Schnorr, Carla Gonçalves Rodrigues & Josimara Wikboldt Schwantz - 2016 - Revista Sul-Americana de Filosofia E Educação 24:157-165.
    A investigação operou por meio dos Ateliês de Escrileituras: Conatus e Rabiscos de sensações na produção de um corpo crianceiro. O trabalho teve por objetivo fazer “escrever a n-1”, segundo um agenciamento rizomático de saberes. Produziram-se escrituras a partir de elementos extraídos da arte, da filosofia e da ciência. Destacam-se os Ateliês na proposta de uma escrita que extraí a unidade da multiplicidade, de uma vida potente e saudável.
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  35.  21
    A Gödel Theorem on Network Complexity Lower Bounds.C. P. Schnorr - 1986 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 32 (19-24):377-384.
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  36.  2
    A Gödel Theorem on Network Complexity Lower Bounds.C. P. Schnorr - 1986 - Mathematical Logic Quarterly 32 (19‐24):377-384.
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  37.  15
    Ciência, tecnologia e sociedade: ensino de Ciências no referencial pós-estruturalista.Samuel Molina Schnorr & Carla Gonçalves Rodrigues - 2017 - Filosofia E Educação 9 (3):46.
    Na presente investigação, objetivou-se analisar, a partir do referencial teórico e metodológico pós-estruturalista, os conceitos de Ciência, Tecnologia e Sociedade na trama com a educação e o ensino de Ciências. Como substrato teórico são utilizadas obras de Michel Foucault, Gilles Deleuze e Felix Guattari, ofertando pistas para ampliar a discussão destes conceitos. Na reunião dos saberes investigados, afirma-se um pensamento científico que desenvolve a produção de sentidos para a educação. Diante do exposto, pensa-se em um ensino, que crie estratégias de (...)
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  38.  14
    Filosofias da diferença e a formação de professores: experimentações com ateliê de escrileituras.Samuel Molina Schnorr, Carla Gonçalves Rodrigues & Josimara Wikboldt Schwantz - 2017 - Educação E Filosofia 31 (61):369-384.
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  39. A possibilidade de pensar a filosofia na perspectiva da diferença: impregnando a formação de professores e experimentando o inédito // The possibility thinking philosophy in perspective of difference.Carla Gonçalves Rodrigues & Schnorr - 2014 - Conjectura: Filosofia E Educação 19 (3):36-49.
    Como a filosofia da diferença pode impregnar a formação de professores nesta contemporaneidade por intermédio de arranjos múltiplos, da disseminação de saberes diversos, dos encontros variados e das composições inéditas, a partir dos passeios urbanos? Eis a questão norteadora da escrita deste texto, iniciada na pesquisa-intervenção denominada Tramas e usos do passeio urbano: por uma estética professoral . Entendendo que os saberes estão sempre se transformando e se relacionando, objetivamos tecer tramas entre a filosofia da diferença, as ciências educativas e (...)
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  40.  26
    Degrees of Monotone Complexity.William C. Calhoun - 2006 - Journal of Symbolic Logic 71 (4):1327 - 1341.
    Levin and Schnorr (independently) introduced the monotone complexity, Km(α), of a binary string α. We use monotone complexity to define the relative complexity (or relative randomness) of reals. We define a partial ordering ≤Km on 2ω by α ≤Km β iff there is a constant c such that Km(α ↾ n) ≤ Km(β ↾ n) + c for all n. The monotone degree of α is the set of all β such that α ≤Km β and β ≤Km (...)
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  41. Peter Kirschenmann.Concepts Of Randomness - 1973 - In Mario Augusto Bunge (ed.), Exact Philosophy; Problems, Tools, and Goals. Boston: D. Reidel. pp. 129.
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  42.  8
    Reference Explained Away: Anaphoric Reference and Indirect.Robert Bb Random - 2005 - In J. C. Beall & B. Armour-Garb (eds.), Deflationary Truth. Open Court. pp. 258.
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  43.  7
    Fandom as Methodology: A Sourcebook for Artists and Writers.Catherine Grant & Kate Random Love (eds.) - 2019 - London: MIT Press.
    An illustrated exploration of fandom that combines academic essays with artist pages and experimental texts. Fandom as Methodology examines fandom as a set of practices for approaching and writing about art. The collection includes experimental texts, autobiography, fiction, and new academic perspectives on fandom in and as art. Key to the idea of “fandom as methodology” is a focus on the potential for fandom in art to create oppositional spaces, communities, and practices, particularly from queer perspectives, but also through transnational, (...)
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  44. Introduction: Fandom as methodology.Catherine Grant & Kate Random Love - 2019 - In Catherine Grant & Kate Random Love (eds.), Fandom as methodology: a sourcebook for artists and writers. Goldsmiths Press.
     
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  45.  18
    Commentary on Risto Naatanen (1990). The role of attention in auditory information processing as revealed by event-related potentials and other brain measures of cognitive fenctiono BBS 13s201-2888. [REVIEW]A. Ryan, R. D. Ryder, L. Schiebinger, P. Singer & Random House - 1991 - Behavioral and Brain Sciences 14:4.
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  46.  40
    Schnorr trivial sets and truth-table reducibility.Johanna N. Y. Franklin & Frank Stephan - 2010 - Journal of Symbolic Logic 75 (2):501-521.
    We give several characterizations of Schnorr trivial sets, including a new lowness notion for Schnorr triviality based on truth-table reducibility. These characterizations allow us to see not only that some natural classes of sets, including maximal sets, are composed entirely of Schnorr trivials, but also that the Schnorr trivial sets form an ideal in the truth-table degrees but not the weak truth-table degrees. This answers a question of Downey, Griffiths and LaForte.
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  47. Schnorr triviality and genericity.Johanna N. Y. Franklin - 2010 - Journal of Symbolic Logic 75 (1):191-207.
    We study the connection between Schnorr triviality and genericity. We show that while no 2-generic is Turing equivalent to a Schnorr trivial and no 1-generic is tt-equivalent to a Schnorr trivial, there is a 1-generic that is Turing equivalent to a Schnorr trivial. However, every such 1-generic must be high. As a corollary, we prove that not all K-trivials are Schnorr trivial. We also use these techniques to extend a previous result and show that the (...)
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  48. Algorithmic Randomness and Probabilistic Laws.Jeffrey A. Barrett & Eddy Keming Chen - manuscript
    We consider two ways one might use algorithmic randomness to characterize a probabilistic law. The first is a generative chance* law. Such laws involve a nonstandard notion of chance. The second is a probabilistic* constraining law. Such laws impose relative frequency and randomness constraints that every physically possible world must satisfy. While each notion has virtues, we argue that the latter has advantages over the former. It supports a unified governing account of non-Humean laws and provides independently motivated (...)
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    The Random Somatic Mutation is not Quite Random.Florentin Smarandache - unknown
    This research note challenges the idea that Random Somatic Mutations are entirely random, highlighting their non-equiprobable nature and their influence on evolution, involution, or indeterminacy. It recalls the Neutrosophic Theory of Evolution, extending Darwin’s theory, and emphasizes the importance of distinguishing between different senses of ‘random mutation’ in evolutionary theory.
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    Randomness is an unavoidably epistemic concept.Edgar Danielyan - 2022 - Annual Review of the Oxford Philosophical Society 2022 (1).
    Are there any truly ontologically random events? This paper argues that randomness is an unavoidably epistemic concept and therefore ascription of ontological randomness to any particular event or series of events can never be justified.
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