The IP theorem, which asserts that IP = PSPACE (Lund et. al., and Shamir, in J. ACM 39(4)), is one of the major achievements of complexity theory. The known proofs of the theorem are based on the arithmetization technique, which transforms a quantified Boolean formula into a related polynomial. The ... more >>>
Properties of Boolean functions on the hypercube that are invariant
with respect to linear transformations of the domain are among some of
the most well-studied properties in the context of property testing.
In this paper, we study a particular natural class of linear-invariant
properties, called matroid freeness properties. These properties ...
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We show that proving results such as BPP=P essentially
necessitate the construction of suitable pseudorandom generators
(i.e., generators that suffice for such derandomization results).
In particular, the main incarnation of this equivalence
refers to the standard notion of uniform derandomization
and to the corresponding pseudorandom generators
(i.e., the standard uniform ...
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