Locally decodable codes (LDCs) are error-correcting codes $ C:\Sigma^ k\to\Sigma^ n $ that
admit a local decoding algorithm that recovers each individual bit of the message by …

Locally correctable codes (LCCs) are error correcting codes which admit local algorithms
that correct any individual symbol of a corrupted codeword via a minuscule number of …

Probabilistically checkable proofs (PCPs) can be verified based only on a constant amount
of random queries, such that any correct claim has a proof that is always accepted, and …

We prove a general structural theorem for a wide family of local algorithms, which includes
property testers, local decoders, and probabilistically checkable proofs of proximity. Namely …

A graph G is called self-ordered (aka asymmetric) if the identity permutation is its only
automorphism. Equivalently, there is a unique isomorphism from G to any graph that is …

We investigate the complexity of solving stable or perturbation-resilient instances of k-means
and k-median clustering in fixed dimension Euclidean metrics (or more generally doubling …

Analog quantum simulations---simulations of one Hamiltonian by another---is one of the
major goals in the noisy intermediate-scale quantum computation (NISQ) era, and has many …

Prior studies of testing graph properties presume that the tester can obtain uniformly
distributed vertices in the tested graph (in addition to obtaining answers to the some type of …

Universal locally testable codes (universal-LTC s), recently introduced in our companion
paper (CJTCS, 2018), are codes that admit local tests for membership in numerous …

This thesis investigates the capabilities of classical and quantum sublinear algorithms
through the lens of complexity theory. The formal classification of problems between …