With Sam Buss and Leszek Kolodziejczyk,
"Fragments of approximate counting",
preprint, 2012
(pdf)
With Bjørn Kjos-Hanssen and Antoine Taveneaux,
"How much randomness is needed for statistics?",
submitted, 2012
(pdf)
"Higher complexity search problems for bounded arithmetic and a formalized no-gap theorem",
in Archive for Mathematical Logic, Vol 50:7-8, 2011,
pages 665-680,
(pdf)
With Pavel Pudlák,
"Alternating minima and maxima, Nash equilibria and Bounded Arithmetic"
(revised 2010),
to appear in Annals of Pure and Applied Logic,
(pdf)
With Leszek Kolodziejczyk and Phuong Nguyen,
"The provably total NP search problems of weak second order
bounded arithmetic" (revised October 2010), in Annals of Pure and Applied
Logic, Vol 162:6, 2011, pages 419-446,
(pdf)
With Alan Skelley,
"The provably total search problems of bounded arithmetic"
(revised March 2010),
in Proceedings of the London Mathematical Society, Vol 103:1, 2011, pages 106-138,
(pdf)
With Leszek Kolodziejczyk,
"The polynomial and linear hierarchies in V0",
in Mathematical Logic Quarterly, Vol 55:5, 2009, pages 509-514
(an earlier version appeared in Proceedings of CiE 2007, LNCS 4497)
(pdf)
With Leszek Kolodziejczyk,
"The polynomial and linear hierarchies in models where the weak
pigeonhole principle fails",
in Journal of Symbolic Logic, Vol 73:2, 2008, pages 578-592,
(pdf)
With Jan Krajicek and Alan Skelley,
"NP search problems in low fragments of bounded arithmetic" (revised September 2006),
in Journal of Symbolic Logic, Vol 72:2, 2007
(postscript)
With Steve Cook, "The replacement scheme in weak arithmetic",
in ACM Transactions on Computational Logic, Vol 7:4, 2006
(postscript at TOCL)
"A note on Delta_1 induction and Sigma_1 collection",
in Fundamenta Mathematicae, Vol 186, 2005
(postscript)
With Nicola Galesi, "Resolution and pebbling games",
SAT 2005
(postscript)
With Michael Soltys, "Weak theories of linear algebra",
in Archive for Mathematical Logic, Vol 44:2, 2005
(postscript)
"Structures interpretable in models of bounded arithmetic",
in Annals of Pure and Applied Logic, Vol 135, 2005
(postscript)
"A model-theoretic characterization of the weak pigeonhole principle",
in Annals of Pure and Applied Logic, Vol 118, 2002
(postscript ,
dvi)
Miscellaneous
"Notes on switching lemmas", manuscript, 2009
(pdf)
"The weak pigeonhole principle in models of bounded arithmetic",
doctoral thesis, University of Oxford, 2002
(postscript,
dvi)
