An introduction to Kolmogorov complexity and its applications
An introduction to Kolmogorov complexity and its applications
Journal of the ACM (JACM)
Bounded arithmetic, propositional logic, and complexity theory
Bounded arithmetic, propositional logic, and complexity theory
On resource-bounded instance complexity
Theoretical Computer Science
On Reducibility to Complex or Sparse Sets
Journal of the ACM (JACM)
NP-Hard Sets Have Many Hard Instances
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Resource-Bounded Kolmogorov Complexity Revisited
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
Complexity Cores and Hard-To-Prove Formulas
CSL '87 Proceedings of the 1st Workshop on Computer Science Logic
A complexity theoretic approach to randomness
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Nondeterministic Instance Complexity and Proof Systems with Advice
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Proof systems that take advice
Information and Computation
Different approaches to proof systems
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
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In this note we first formalize the notion of hard tautologies using a nondeterministic generalization of instance complexity. We then show, under reasonable complexity-theoretic assumptions, that there are infinitely many propositional tautologies that are hard to prove in any sound propositional proof system.