BSF:2014359:Invariance in error correcting codes and computational complexity

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Information can be digitally encoded (as 0s and 1s) so that even if some of these bits are lost or modified, the information can be recovered. This foundational idea, which is the basis for such commonplace technologies as DVDs and digital broadcast, is explored in theoretical computer science, where it plays a key role in probabilistically checkable proofs and property testing. Exploring the limits of this idea in these abstract settings can lead to new understanding, which enables technological innovation. It has been long known in mathematics that studying the invariances (symmetries) of an object has an important role in understanding the object. In recent years, the study of invariances has led to some significant advances in various topics in theoretical computer science, such as property testing, error-correcting codes and complexity theory. For example, codes with affine invariance and codes with a transitive invariance group have been shown to have important applications in complexity theory, such as constructing PCPs. This project will support the travel of the PIs and their students for research collaborations on these topics with collaborators in Israel. This research will deepen our understanding of objects with invariances, and develop new applications of this theory in complexity theory.