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The flexible logic circuit configured using Si-based memristive switches is demonstrated. The memristive switches consisting of Ag/a-Si/heavily doped p-type Si are constructed on plastic using top-down-fabricated Si nanowires. The logic gate analyses provide insight toward logic circuits having multifunctionality and high connectivity through a crossbar-array architecture. With the strong stability of the logic performances against external strain, the memristive switch looks promising as a building block for flexible electronics.