Propositional proof complexity is an area of complexity theory that addresses the question of whether the class NP is closed under complement, and also provides a theoretical framework for studying practical applications such as SAT solving.
Some of the most well-studied contradictions are random $k$-CNF formulas where each clause of ... more >>>

A propositional proof system based on ordered binary decision diagrams (OBDDs) was introduced by Atserias et al. Krajicek proved exponential lower bounds for a strong variant of this system using feasible interpolation, and Tveretina et al. proved exponential lower bounds for restricted versions of this system for refuting formulas derived ... more >>>

This paper is motivated by a conjecture that BPP can be characterized in terms of polynomial-time nonadaptive reductions to the set of Kolmogorov-random strings. In this paper we show that an approach laid out by [Allender et al] to settle this conjecture cannot succeed without significant alteration, but that it ... more >>>

Can complexity classes be characterized in terms of efficient reducibility to the (undecidable) set of Kolmogorov-random strings? Although this might seem improbable, a series of papers has recently provided evidence that this may be the case. In particular, it is known that there is a class of problems $C$ defined ... more >>>

Let C(x) and K(x) denote plain and prefix Kolmogorov complexity, respectively, and let R_C and R_K denote the sets of strings that are ``random'' according to these measures; both R_K and R_C are undecidable. Earlier work has shown that every set in NEXP is in NP relative to both R_K ... more >>>

In this paper we give an exposition of a theorem by Muchnik and Positselsky, showing that there is a universal prefix Turing machine U, with the property that there is no truth-table reduction from the halting problem to the set {(x,i) : there is a description d of length at ... more >>>