We consider some problems about pairs of disjoint $NP$ sets. The theory of these sets with a natural concept of reducibility is, on the one hand, closely related to the theory of proof systems for propositional calculus, and, on the other, it resembles the theory of NP completeness. Furthermore, such ... more >>>

We define propositional quantum Frege proof systems and compare it with classical Frege proof systems. more >>>

Motivated by strong Karp-Lipton collapse results in bounded arithmetic, Cook and Krajicek have recently introduced the notion of propositional proof systems with advice. In this paper we investigate the following question: Do there exist polynomially bounded proof systems with advice for arbitrary languages? Depending on the complexity of the underlying ... more >>>