Let C={c_1,...,c_n} be a set of constraints over a set of
variables. The {\em satisfiability-gap} of C is the smallest
fraction of unsatisfied constraints, ranging over all possible
assignments for the variables.

We prove a new combinatorial amplification lemma that doubles the
satisfiability-gap of a constraint-system, with only a linear ... more >>>

We introduce a new measure notion on small complexity classes (called F-measure), based on martingale families,
that get rid of some drawbacks of previous measure notions:
martingale families can make money on all strings,
and yield random sequences with an equal frequency of 0's and 1's.
As applications to F-measure,
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In this work we study two seemingly unrelated notions. Locally Decodable Codes(LDCs) are codes that allow the recovery of each message bit from a constant number of entries of the codeword. Polynomial Identity Testing (PIT) is one of the fundamental problems of algebraic complexity: we are given a circuit computing ... more >>>