Complexity measures for public-key cryptosystems
SIAM Journal on Computing - Special issue on cryptography
Oracles for structural properties: the isomorphism problem and public-key cryptography
Journal of Computer and System Sciences
On reducibility and symmetry of disjoint NP pairs
Theoretical Computer Science - Mathematical foundations of computer science
Optimal proof systems imply complete sets for promise classes
Information and Computation
SIAM Journal on Computing
Properties of NP-Complete Sets
SIAM Journal on Computing
Canonical disjoint NP-pairs of propositional proof systems
Theoretical Computer Science
The complexity of unions of disjoint sets
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Disjoint NP-pairs from propositional proof systems
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Hi-index | 0.00 |
We investigate the connection between propositional proof systems and their canonical pairs. It is known that simulations between proof systems translate to reductions between their canonical pairs. We focus on the opposite direction and study the following questions. Q1: Where does the implication [can(f) ≤mpp can(g) ⇒ f ≤s g] hold, and where does it fail? Q2: Where can we find proof systems of different strengths, but equivalent canonical pairs? Q3: What do (non-)equivalent canonical pairs tell about the corresponding proof systems? Q4: Is every NP-pair (A,B), where A is NP-complete, strongly manyone equivalent to the canonical pair of some proof system? In short, we show that both parts of Q1 and Q2 can be answered with 'everywhere', which generalize previous results by Pudlák and Beyersdorff. Regarding Q3, inequivalent canonical pairs tell that the proof systems are not "very similar", while equivalent, P-inseparable canonical pairs tell that they are not "very different". We can relate Q4 to the open problem in structural complexity that asks whether unions of disjoint NP-complete sets are NP-complete. This demonstrates a new connection between proof systems, disjoint NP-pairs, and unions of disjoint NP-complete sets.