Proof systems that take advice

These results show that providing proof systems with advice yields a more powerful model, but this model is also less directly applicable in practice. Our third question therefore asks whether the usage of advice in propositional proof systems can be simplified or even eliminated. While in principle, the advice can be very complex, we show that propositional proof systems with logarithmic advice are also computable in poly-time with access to a sparse NP-oracle. Employing a recent technique of Buhrman and Hitchcock [CCC, 2008] we also manage to transfer the advice from the proof to the proven formula, which leads to a more practical computational model.