Sublattices of the polynomial time degrees
Information and Control
Structural complexity 1
On the Structure of Polynomial Time Reducibility
Journal of the ACM (JACM)
On the Complexity of Resolution with Bounded Conjunctions
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Optimal Proof Systems for Propositional Logic and Complete Sets
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Complete Problems for Promise Classes by Optimal Proof Systems for Test Sets
COCO '98 Proceedings of the Thirteenth Annual IEEE Conference on Computational Complexity
On the lengths of proofs in the propositional calculus (Preliminary Version)
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
On the lengths of proofs in the propositional calculus.
On the lengths of proofs in the propositional calculus.
On optimal algorithms and optimal proof systems
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Canonical disjoint NP-pairs of propositional proof systems
Theoretical Computer Science
Canonical disjoint NP-Pairs of propositional proof systems
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Survey of disjoint NP-pairs and relations to propositional proof systems
Theoretical Computer Science
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We examine the degree structure of the simulation relation on the proof systems for a set L. As observed, this partial order forms a distributive lattice. A greatest element exists iff L has an optimal proof system. In case L is infinite there is no least element, and the class of proof systems for L is not presentable. As we further show the simulation order is dense. In fact any partial order can be embedded into the interval determined by two proof systems f and g such that f simulates g but g does not simulate f. Finally we obtain that for any non-optimal proof system h an infinite set of proof systems that are pairwise incomparable with respect simulation and that are also incomparable to h.