We study the testing problem, that is, the problem of determining (maybe
probabilistically) if a function to which we have oracle access
satisfies a given property.

We propose a framework in which to formulate and carry out the analyzes
of several known tests. This framework establishes a connection between
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Locally testable codes (LTCs) are error-correcting codes for which membership, in the code, of a given word can be tested by examining it in very few locations. Most known constructions of locally testable codes are linear codes, and give error-correcting codes
whose duals have (superlinearly) {\em many} small weight ... more >>>