An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Communication complexity
Communication complexity of document exchange
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
New applications of the incompressibility method: part II
Theoretical Computer Science - Selected papers in honor of Manuel Blum
Distributed Algorithms
Conditional complexity and codes
Theoretical Computer Science
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Kolmogorov's structure functions and model selection
IEEE Transactions on Information Theory
Kolmogorov Complexity and Combinatorial Methods in Communication Complexity
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Kolmogorov complexity and combinatorial methods in communication complexity
Theoretical Computer Science
Interactive information complexity
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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We initiate the theory of communication complexity of individual inputs held by the agents. This contrasts with the usual communication complexity model, where one counts the amount of communication for the worst-case or the average-case inputs. The individual communication complexity gives more information (the worst-case and the average-case can be derived from it but not vice versa) and may in some cases be of more interest. It is given in terms of the Kolmogorov complexities of the individual inputs. There are different measures of communication complexity depending on whether the protocol is guaranteed to be correct for all inputs or not, and whether there's one-way or two-way communication. Bounds are provided for the communication of specific functions and connections between the different communication measures are shown. Some counter-intuitive results: for deterministic protocols that need to communicate Bob's input to Alice they need to communicate all of Bob's input (rather than the information difference with Alice's input), and there are so-called ''non-communicable'' inputs.