We initiate a study of non-interactive proofs of proximity. These proof-systems consist of a verifier that wishes to ascertain the validity of a given statement, using a short (sublinear length) explicitly given proof, and a sublinear number of queries to its input. Since the verifier cannot even read the entire ... more >>>

We prove that $T_{NC^1}$, the true universal first-order theory in the language containing names for all uniform $NC^1$ algorithms, cannot prove that for sufficiently large $n$, SAT is not computable by circuits of size $n^{2kc}$ where $k\geq 1, c\geq 4$ unless each function $f\in SIZE(n^k)$ can be approximated by formulas ... more >>>

We give several improvements on the known hardness of the unique shortest vector problem in lattices, i.e., the problem of finding a shortest vector in a given lattice given a promise that the shortest vector is unique upto a uniqueness factor $\gamma$.
We give a deterministic reduction from the ... more >>>