This note refers to the effect of the proximity parameter on the operation of (standard) property testers. Its bottom-line is that, except in pathological cases, the effect of the proximity parameter is restricted to determining the query complexity of the tester. The point is that, in non-pathological cases, the mapping ... more >>>

We develop a new notion called {\it tester of a class $\cM$ of
functions} $f:\cA\to \cC$ that maps the elements $\bfa\in \cA$ in
the domain $\cA$ of the function to a finite number (the size of
the tester) of elements $\bfb_1,\ldots,\bfb_t$ in a smaller
sub-domain $\cB\subset \cA$ where the property ... more >>>

We address the following problem: how to execute any algorithm P, for an unbounded number of executions, in the presence of an adversary who observes partial information on the internal state of the computation during executions. The security guarantee is that the adversary learns nothing, beyond P's input/output behavior.

This ... more >>>