We prove that the proof system OBDD(and, weakening) is not automatable unless P = NP. The proof is based upon the celebrated result of Atserias and Muller [FOCS 2019] about the hardness of automatability for resolution. The heart of the proof is lifting with a multi-output indexing gadget from resolution ... more >>>

In their highly influential paper, Ben-Sasson, Goldreich, Harsha, Sudan, and Vadhan (STOC 2004) introduced the notion of a relaxed locally decodable code (RLDC). Similarly to a locally decodable code (Katz-Trevisan; STOC 2000), the former admits access to any desired message symbol with only a few queries to a possibly corrupted ... more >>>

Given query access to a monotone function $f\colon\{0,1\}^n\to\{0,1\}$ with certificate complexity $C(f)$ and an input $x^{\star}$, we design an algorithm that outputs a size-$C(f)$ subset of $x^{\star}$ certifying the value of $f(x^{\star})$. Our algorithm makes $O(C(f) \cdot \log n)$ queries to $f$, which matches the information-theoretic lower bound for this ... more >>>