Selected Publications
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Chaitin's halting probability and the compression of strings using oracles with Andrew E.M. Lewis Proceedings of the Royal Society (in press). Format: PDF Summary |
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Randomness Notions and Partial Relativization with Joe Miller and Andre Nies Israel Journal of Mathematics (in press). Format: PDF Summary |
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Measure and Cupping in the Turing Degrees with Andrew E.M. Lewis Proceedings of the American Mathematical Society (in press). Format: PDF Summary |
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Jump inversions inside effectively closed sets and applications to randomness with Rod Downey and Keng-Meng Ng Journal of Symbolic Logic (in press) Format: PDF Summary |
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Working with strong reducibilities above totally $\omega$-c.e. and array computable degrees with Rod Downey and Noam Greenberg Transactions of the American Mathematical Society. 362 (2010), 777-813. Format: PDF Summary |
Selected Talks
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Kolmogorov complexity and computably enumerable sets: Questions and directions Meeting: Dagstuhl, Germany. Year: 2012 Format: PDF |
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Measures of relative complexity Meeting: The Mathematical Legacy of Alan Turing (Public opening of the SAS programme, Spitalfields Day) Year: 2012 Format: PDF |
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Chaitin's halting probability and the compression of strings using oracles Meeting: Logic Colloquium, Barcelona. Year: 2011 Format: PDF |
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On the number of sequences with trivial initial segment complexity Meeting: 8th Panhellenic Logic Conference Year: 2011 Format: PDF |
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Definability and weak reducibilities in
algorithmic randomness Meeting: 5th Conference on Logic, Computability and Randomness Year: 2010 Format: PDF |
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Randomness and Partial Relativization Meeting: European Logic Colloquium (ASL meeting), Sofia Year: 2009 Format: PDF |
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Tracing and domination in the Turing degrees Meeting: 11th Asian Logic Colloquium, Singapore and CiE conference, Heidelberg Year: 2009 Format: PDF |
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Degrees of computability and degrees of compressibility Meeting: 4th Conference on Logic Computability and Randomness, Marseille, France Year: 2009 Format: PDF |
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Computability and Randomness Meeting: Logic seminar in the University of North Texas Year: 2009 Format: PDF |
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PA degrees, $\Pi^0_1$ classes and Relative Randomness Meeting: Computability and Randomness, Nanjing, China Year: 2008 Format: PDF |
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Randomness, Lowness and Degrees Meeting: Theory and Applications of Models of Computation Shanghai, China Year: 2007 Format: PDF |
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Computably enumerable splittings, randomness and lowness Meeting: Computability and Randomness workshop, Auckland New Zealand Year: 2007 Format: PDF |
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Relative Randomness and cardinality Meeting: NZ math society and AMS 1st joint meeting, Wellington, New Zealand Year: 2007 Format: PDF |
Solved Problems from the literature
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Are all almost everywhere dominating degrees array non-computable?
Problem 8.6.4 in Nies' book Computability and Randomness Solution: Summary PDF |
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What is the arithmetical complexity of the number of K-trivial sets with a given constant?
Problem 5.2.16 in Nies' book Computability and Randomness and a question in
Section 10.1.4 of the book
Algorithmic Randomness and Complexity
by Downey/Hirschfeldt Solution: Summary PDF |
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Does van Lambalgen's theorem hold for weak 2-randomness?
Problem 3.6.9 in Nies' book Computability and Randomness Solution: Summary PDF |
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Are all weakly 2-random sets array computable?
Problem 8.2.14 in Nies' book Computability and Randomness Solution: Summary PDF |
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In the LR degrees, can the degree of a weakly 2-random set be below the degree of the halting problem?
Problem 5.6.16 in Nies' book Computability and Randomness Solution: Summary PDF |
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Are the low for Omega LK degrees exactly the ones with countably many predecessors?
Problem 8.1.13 in Nies' book Computability and Randomness
and in "Joseph S. Miller. The K-degrees, low for K degrees, and weakly low for K sets. Notre
Dame J. Formal Logic, 50(4):381--391, 2010." Solution: Summary PDF |
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Can an almost everywhere dominating function have minimal Turing degree?
A question of Simpson Solution: Summary PDF |
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Is there a proper prime $\Sigma^0_4$ ideal in the c.e. degrees?
A question of Calhoun in "Incomparable prime ideals of recursively enumerable degrees. Ann. Pure
Appl. Logic, 63(1):39--56, 1993." Solution: Summary PDF |
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What is the measure of the Turing degrees which satisfy the cupping property?
A question of Jockusch Solution: Summary PDF |
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Are there c.e. reals that form a minimal pair in the $K$-degrees?
A question of Downey and Hirschfeldt from their book "Algorithmic randomness and complexity" Solution: Summary PDF |