We prove that Perfect Matching in bipartite planar graphs is in UL, improving upon
the previous bound of SPL (see [DKR10]) on its space complexity. We also exhibit space
complexity bounds for some related problems. Summarizing, we show that, constructing:
1. a Perfect Matching in bipartite planar graphs is in ... more >>>

The main open problem in the area of locally testable codes (LTCs) is whether there exists an asymptotically good family of LTCs and to resolve this question it suffices to consider the case of query complexity $3$. We argue that to refute the existence of such an asymptotically good family ... more >>>

Locally testable codes, i.e., codes where membership in the code is testable with a constant number of queries, have played a central role in complexity theory. It is well known that a code must be a "low-density parity check" (LDPC) code for it to be locally testable, but few LDPC ... more >>>