Publications in Journals

On the number of infinite sequences with trivial initial segment complexity with Tom Sterkenburg Theoretical Computer Science 412 (2011) 7133-7146. Format: PDF Summary

Universality probability of a prefix-free machine with David L. Dowe Philosophical Transactions of the Royal Society (in press) Format: PDF Summary

Chaitin's halting probability and the compression of strings using oracles with Andrew E.M. Lewis Proc. R. Soc. A (2011) 467, 2912-2926. Format: PDF Summary

Kolmogorov complexity of initial segments of sequences and arithmetical definability with Charlotte Vlek Theoretical Computer Science 412 (2011) 5656-5667 Format: PDF Summary

Strings with trivial Kolmogorov Complexity International Journal of Software and Informatics, Volume 5, Issue 4 (2011), pp. 609-623 Format: PDF Summary

Measure and Cupping in the Turing Degrees with Andrew E.M. Lewis Proceedings of the American Mathematical Society (in press). Format: PDF Summary

Randomness Notions and Partial Relativization with Joe Miller and Andre Nies Israel Journal of Mathematics (in press). Format: PDF Summary

Upper bounds on ideals in the Turing degrees with Andre Nies Annals of Pure and Applied Logic 162 (2011) 465-473. Format: PDF Summary

Jump inversions inside effectively closed sets and applications to randomness with Rod Downey and Keng-Meng Ng J. Symb. Log. 76(2): 491-518 (2011) Format: PDF Summary

Tracing and domination in the Turing degrees Annals of Pure and Applied Logic 163 (2012): 500-505. Format: PDF Summary

Lower bounds in the Turing degrees revisited with Andre Nies Journal of Logic and Computation (in press) Format: PDF Summary

Elementary differences between the degrees of unsolvability and degrees of compressibility Annals of Pure and Applied Logic 161 (2010) 923-934 Format: PDF Summary

Compactness arguments with effectively closed sets for the study of relative randomness Journal of Logic and Computation (in press) Format: PDF Summary

Relative randomness and cardinality Notre Dame Journal of Formal Logic 51 Number 2 (2010) Format: PDF Summary

K-trivial degrees and the jump-traceability hierarchy with Rod Downey and Noam Greenberg Proceedings of the American Mathematical Society. 137 (2009) no. 6, 2099-2109 Format: PDF Summary

The Importance of $\Pi^0_1$ Classes in Effective Randomness with A. Lewis and K.-M. Ng Journal of Symbolic Logic. Volume 75, Number 1 (2010) Format: PDF Summary

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

Non-Cupping, Measure and Computably Enumerable Splittings with Anthony Morphett Mathematical Structures in Computer Science. vol. 19 (2009) 25-43 Format: PDF Summary

$\Pi^0_1$ classes, LR degrees and Turing degrees with Andy Lewis and Frank Stephan Annals of Pure and Applied Logic. Volume 156, Issue 1 (2008) pages 21-38 Format: PDF Summary

$K$-triviality of closed sets and continuous functions with D. Cenzer, J. Remmel and R. Weber Journal of Logic and Computation 19 (2009), no. 1, 3-16 Format: PDF Summary

Randomness, Lowness and Degrees with Andy Lewis and Mariya Soskova Journal of Symbolic Logic. vol.73, Issue 2, pp. 559-577 (2008) Format: PDF Summary

Algorithmic Randomness of Closed Sets with Paul Brodhead, Douglas Cenzer, Seyyed Dashti and Rebecca Weber Journal of Logic and Computation 2007 17:1041-1062. Format: PDF Summary

Algorithmic Randomness of Continuous Functions with P. Brodhead, D. Cenzer, J.B. Remmel and R. Weber Archive for Mathematical Logic, Volume 46, Numbers 7-8, May 2008 Format: PDF Summary

Post's Programme for the Ershov Hierarchy with Bahareh Afshari, S.~Barry Cooper and Frank Stephan Journal of Logic and Computation 2007 17:1025-1040. Format: PDF Summary

Randomness and the Linear degrees of computability with Andy Lewis Annals of Pure and Applied Logic Volume 145, Issue 3, (2007), pages 252-257 Format: PDF Summary

Random Non-Cupping Revisited Journal of Complexity 22 (2006) 850-857. Format: PDF Summary

The Hypersimple-free c.e. wtt degrees are dense in the c.e. wtt degrees with Andy Lewis Notre Dame Journal of Formal Logic Volume 47 Issue 3 (2006) Format: PDF Summary

A c.e. real that cannot be sw-computed by any $\Omega$ number with Andy Lewis Notre Dame Journal of Formal Logic Volume 47 Issue 2 (2006) Format: PDF Summary

Random Reals and Lipschitz Continuity with Andy Lewis Mathematical Structures in Computer Science Volume 16, issue 5 (2006) Format: PDF Summary

The $ibT$ Degrees of C.E. Sets are Not Dense with Andy Lewis Annals of Pure and Applied Logic Volume 141, Issues 1-2, 2006 Format: PDF Summary

Hypersimplicity and Semicomputability in the Weak Truth Table Degrees Archive for Math. Logic Vol.44, Number 8 (2005) 1045-1065 Format: PDF Summary

$h$-Monotonically Computable Real Numbers with X. Zheng and R. Rettinger Mathematical Logic Quarterly, Vol.51 No.2 157-170 (2005) Format: PDF Summary

Approximation representations for reals and their wtt degrees Mathematical Logic Quarterly, Vol. 50 number 4/5 (2004) 370-380 Format: PDF Summary

Approximation representations for $\Delta_2$ reals Archive for Math. Logic, Volume 43, Number 8, (2004) p. 947-964 Format: PDF Summary

The approximation structure of a computably approximable real J. Symbolic Logic, Vol.68, no.3 (2003) 885-922 Format: PDF Summary

A transfinite hierarchy of reals Mathematical Logic Quarterly, Vol. 49, Number 2 (2003) 163-172. Format: PDF Summary

Publications in Conference Proceedings

K-trivials are never continuously random with N. Greenberg, A. Montalban and T. Slaman Proceedings of the 11th Asian Logic Conference. World Scientific. Format: PDF Summary

A cappable almost everywhere dominating computably enumerable degree with Antonio Montalban Electronic Notes in Theoretical Computer Science Volume 167 (2007) Format: PDF Summary

Computably enumerable sets in the Solovay and the Strong Weak Truth Table Degrees LNCS Volume 3526, Proceedings of the CiE conference 2005 conference in Amsterdam (2005) 8-17 Format: PDF Summary

Extended abstracts in Conference Proceedings

$K$-trivial closed sets and continuous functions with D. Cenzer, J. Remmel and R. Weber CIE 2007, Computation and Logic in the Real World, Third Computability in Europe conference, Siena, Italy, June 2007, S.B. Cooper, B. Loewe and A. Sorbi (Eds.) Springer Lecture Notes in Computer Science 4497 (2007), 135-145. Format: PDF Summary

Working with the LR Degrees with Andy Lewis, Mariya Soskova Theory and Applications of Models of Computation: 4th International Conference TAMC 2007, Shanghai, China, May 2007, Proceedings (J.-Y. Cai, S.B. Cooper, H. Zhu) Springer Lecture Notes in Computer Science, LNCS 4484, 2007 Format: PDF Summary

Immunity properties and the n-c.e. hierarchy with Bahareh Afshari and S. Barry Cooper Proceedings of the Third Annual Conference on Theory and Applications of Models of Computation TAMC06, Beijing, May 2006 (Jin-Yi Cai, S. Barry Cooper, Angsheng Li) Springer Lecture Notes in Computer Science. Format: PDF Summary

On the Monotonic Computability of Semi-computable Real Numbers with Xizhong Zheng Lecture Notes in Computer Science, Springer-Verlag, Heidelberg, Volume 2731 / 2003, p.290-300 Format: PDF Summary

On 0'-computable reals Electronic Notes in Theoretical Computer Science, Vol.66, Issue 1, Eds. V. Brattka, M. Schroder and K. Weihrauch, Elsevier Science Publishers, 2002. Summary

Reviews

Review of Lerman's "A framework for priority arguments" (Lecture Notes in Logic vol. 34. Cambridge University Press, NY, 2010, xvi + 176 pp.) Bulletin of Symbolic Logic, Volume 17 (2011), Issue 3, pp. 464-467. Format: PDF

Recent Papers

Kolmogorov complexity and computably enumerable sets with Angsheng Li Submitted. Format: PDF Summary

The typical Turing degree with A. R. Day and A.E.M. Lewis Submitted. Format: PDF Summary

Universal computably enumerable sets and initial segment prefix-free complexity Submitted. Format: PDF Summary

On the gap between trivial and nontrivial initial segment prefix-free complexity with Martijn Baartse Submitted. Format: PDF Summary

PhD Thesis:

Computability and Applications to Analysis University of Leeds, July 2004 Format: PDF