We establish strong inapproximability for finding the sparsest nonzero vector in a real subspace (where sparsity refers to the number of nonzero entries). Formally we show that it is NP-Hard (under randomized reductions) to approximate the sparsest vector in a subspace within any constant factor. By simple tensoring the inapproximability ... more >>>

Two matrices are said to be principal minor equivalent if they have equal
corresponding principal minors of all orders. We give a characterization of
principal minor equivalence and a deterministic polynomial time algorithm to
check if two given matrices are principal minor equivalent. Earlier such
results were known for ... more >>>

We show that every NP relation that can be verified by a bounded-depth polynomial-sized circuit, or a bounded-space polynomial-time algorithm, has a computational zero-knowledge proof (with statistical soundness) with communication that is only additively larger than the witness length. Our construction relies only on the minimal assumption that one-way functions ... more >>>