Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Journal of the ACM (JACM)
The complexity of Boolean functions
The complexity of Boolean functions
The complexity of finite functions
Handbook of theoretical computer science (vol. A)
Taking it to the limit: on infinite variants of NP-complete problems
Journal of Computer and System Sciences
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
A Topological View of Some Problems in Complexity Theory
Proceedings of the Mathematical Foundations of Computer Science 1984
Some connections between nonuniform and uniform complexity classes
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Borel sets and circuit complexity
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
A clique problem equivalent to graph isomorphism
ACM SIGACT News
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Motivated by the analogy "(NP/Poly) ∼ analytic", we propose a co-analytic set W whose finite equivalent Wfinite is coNP-complete. The complement of W is in fact a variant of "infinite clique". A combinatorial proof of the non-analyticity of W is produced and studied in order to be (eventually) "finitized" into a probabilistic proof of "Wfinite ∉NP/Poly (this would imply NP ≠ CoNP). A reasonable objective could be to determine a specific class of nondeterministic circuits which allow a finitization of the arguments of the infinite case, and thus which cannot compute Wfinite.