Lifting with Inner Functions of Polynomial Discrepancy
Lifting theorems are theorems that bound the communication complexity of a composed function f∘gⁿ in terms of the query complexity of f and the communication complexity of g. Such theorems constitute a powerful generalization of direct-sum theorems for g, and have seen numerous applications in recent years.
We prove a new lifting theorem that works for every two functions f,g such that the discrepancy of g is at most inverse polynomial in the input length of f. Our result is a significant generalization of the known direct-sum theorem for discrepancy, and extends the range of inner functions g for which lifting theorems hold.
Lifting
communication complexity
query complexity
discrepancy
Theory of computation~Communication complexity
Theory of computation~Oracles and decision trees
26:1-26:17
RANDOM
Yahel
Manor
Yahel Manor
Department of Computer Science, University of Haifa, Israel
Supported by the Israel Science Foundation (grant No. 716/20).
Or
Meir
Or Meir
Department of Computer Science, University of Haifa, Israel
https://cs.haifa.ac.il/~ormeir/
https://orcid.org/0000-0001-5031-0750
Partially supported by the Israel Science Foundation (grant No. 716/20).
10.4230/LIPIcs.APPROX/RANDOM.2022.26
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Yahel Manor and Or Meir
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