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Dag-like communication protocols, a generalization of the classical tree-like communication protocols, are useful objects in the realm of proof complexity (most importantly for monotone feasible interpolation) and circuit complexity. We consider three kinds of protocols in this paper (d is the...
CCCatalytic branching programs (catalytic bps) compute the same n-bit boolean function f at multiple entry points that need to be remembered at the exit nodes of the bp. When a doubly exponential number of entry points is allowed, linear amortized catalytic bp size is known to be achievable for...
We study the problem of finding K collision pairs in a random function f: [N] → [N] by using a quantum computer. We prove that the number of queries to the function in the quantum random oracle model must increase significantly when the size of the available memory is limited. Namely, we...
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