The query complexity of certification

  title={The query complexity of certification},
  author={Guy Blanc and Caleb M. Koch and Jane Lange and Li-Yang Tan},
  journal={Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing},
  • Guy BlancCaleb M. Koch Li-Yang Tan
  • Published 19 January 2022
  • Computer Science, Mathematics
  • Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing
We study the problem of certification: given queries to a function f : {0,1}n → {0,1} with certificate complexity ≤ k and an input x⋆, output a size-k certificate for f’s value on x⋆. For monotone functions, a classic local search algorithm of Angluin accomplishes this task with n queries, which we show is optimal for local search algorithms. Our main result is a new algorithm for certifying monotone functions with O(k8 logn) queries, which comes close to matching the information-theoretic… 
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