5 research outputs found
Hard instances of algorithms and proof systems
"Vegeu el resum a l'inici del document del fitxer adjunt"
Upward Translation of Optimal and P-Optimal Proof Systems in the Boolean Hierarchy over NP
We study the existence of optimal and p-optimal proof systems for classes in
the Boolean hierarchy over . Our main results concern
, i.e., the second level of this hierarchy:
If all sets in have p-optimal proof systems, then all sets in
have p-optimal proof systems. The analogous implication for
optimal proof systems fails relative to an oracle.
As a consequence, we clarify such implications for all classes
and in the Boolean hierarchy over : either we can
prove the implication or show that it fails relative to an oracle. Furthermore,
we show that the sets and have p-optimal proof
systems, if and only if all sets in the Boolean hierarchy over
have p-optimal proof systems which is a new characterization of a conjecture
studied by Pudl\'ak