Complexity Theory in Feasible Mathematics, PhD thesis, August 2014 Logical strength of complexity theory and a formalization of the PCP theorem in bounded arithmetic, Logical Methods in Computer Science, 11(2), 2015; (preprint June 2014) A PVproof of the PCP theorem. Circuit lower bounds in bounded arithmetics, Annals of Pure and Applied Logic, 166(1), 2015; (preprint May 2013)Theories weaker than PV cannot prove polynomial circuit lower bounds on SAT unless psize circuits can be approximated by weaker computational models. Hard tautologies, MSc thesis, May 2011NisanWigderson generators in proof systems with forms of interpolation, Mathematical Logic Quarterly, 57(4), 2011; (preprint March 2010) This shows that Razborov's conjecture about NWgenerators holds for systems admitting feasible interpolation, i.e. suitable NWgenerators based on hard functions are hard for such systems. Bounded arithmetic and theory of Razborov and Rudich, Bc thesis, May 2009
