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Lower Bounds and Identity Testing for Arithmetic Circuits

Final Report Summary - LBITAC (Lower Bounds and Identity Testing for Arithmetic Circuits)

The project studied fundamental problems in algebraic complexity. This is the field whose aim is to understand the intrinsic complexity of computational problems with an algebraic flavor. The most notable questions in this area are proving lower bounds on the size of arithmetic circuits (i.e. showing that some algebraic expressions are very hard to compute) and verifying deterministically whether two algebraic expressions, given in some form, are in fact equivalent. The project obtained state of the art results on all fronts developing new techniques and showing connections to other areas of study such as algebraic geometry, coding theory and signal processing. The fundamental nature of the problems studied in this project enabled us to contribute to other fields. In particular we gave the best known algorithms for decoding a well studied algebraic family of codes from random errors.