Quantum Algorithm for Generalized Deutsch-Jozsa Problem
  We generalize the Deutsch-Jozsa problem and present a quantum algorithm that can solve the generalized Deutsch-Jozsa problem by a single evaluation of a given function. We discuss the initialization of an auxiliary register and present a generalized Deutsch-Jozsa algorithm that requires no initialization of an auxiliary register. 
Dong Pyo Chi, Jinsoo Kim, Soojoon Lee