Gillat Kol (IAS) joint work with Anat Ganor (Weizmann) Ran Raz (Weizmann + IAS) Exponential Separation of Information and Communication

Information theory was developed by Claude Shannon to study one-way data transmission “A mathematical theory of communication” 1948 It had a profound impact on many fields of science. Specifically, it is an incredibly useful tool in TCS Recently, computational aspects of information theory are studied as a goal in its own right Information Theory

Interactive protocols performing a computation are central in TCS ( interactive proofs, communication complexity, cryptography, distributed computing, …) Interactive information theory extends classical information theory to the interactive setting, where information flows in several directions Interactive coding (cf. noisy coding) Interactive compression (cf. data compression) … Interactive Information Theory this talk

Data Compression Entropy function “unpredictability”

Data Compression Theorem [S‘48,H‘52]: Any message can be compressed to its “information content” Interactive Compression Problem [BBCR‘09]: Assume Alice and Bob engage in an interactive communication protocol (i.e., conversation). Can the protocol’s transcript be compressed to its “information content”?

Communication Complexity [Yao‘79] adaptive! Protocol:

Distributional CC

Information Cost The amount of information players learn about each other’s input from the interaction mutual information

Information Cost The amount of information players learn about each other’s input from the interaction

Amount of information revealed Number of bits exchanged

Why is the Interactive Case More Challenging?

Tight!

Direct Sum [80’s] Corollary of Our Result: Strong Direct Sum doesn’t hold!

Underlying Tree multilayer c

Underlying Tree multilayer c

Typical Vertices

multilayer i Typical Vertices typical leaves ≥ 80% correct children typical vertices

multilayer i typical leaves

multilayer i

noisy multilayer i

noisy multilayer i typical leaves

Bursting Noise Game noisy multilayer i typical leaves

noisy multilayer i typical leaves

The Protocol (-bug fix) typical leaves noisy multilayer i 90%10%

Why 90% and not 100%?? typical leaves noisy multilayer i

typical leaves noisy multilayer i

Thank You!