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 >>>

Given two testable properties $\mathcal{P}_{1}$ and $\mathcal{P}_{2}$, under what conditions are the union, intersection or set-difference
of these two properties also testable?
We initiate a systematic study of these basic set-theoretic operations in the context of property
testing. As an application, we give a conceptually different proof that linearity is ... more >>>

In previous works, Juba and Sudan (STOC 2008) and Goldreich, Juba and Sudan (ECCC TR09-075) considered the idea of "semantic communication", wherein two players, a user and a server, attempt to communicate with each other without any prior common language (or communication protocol). They showed that if communication was goal-oriented ... more >>>