An error-correcting code $C \subseteq \F^n$ is called $(q,\epsilon)$-strong locally testable code (LTC) if there exists a tester that makes at most $q$ queries to the input word. This tester accepts all codewords with probability 1 and rejects all non-codewords $x\notin C$ with probability at least $\epsilon \cdot \delta(x,C)$, where ... more >>>

We study the complexity of computing Boolean functions on general
Boolean domains by polynomial threshold functions (PTFs). A typical
example of a general Boolean domain is $\{1,2\}^n$. We are mainly
interested in the length (the number of monomials) of PTFs, with
their degree and weight being of secondary interest. We ... more >>>

We study the power of Arthur-Merlin probabilistic proof systems in the data stream model. We show a canonical $\mathcal{AM}$ streaming algorithm for a wide class of data stream problems. The algorithm offers a tradeoff between the length of the proof and the space complexity that is needed to verify it.

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