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We analyze the optical signal processing functionality of periodic structures consisting of alternating layers of materials possessing opposite Kerr nonlinearities. By elaborating an analytical model and employing numerical simulations, we explore the performance of proposed passive optical limiters and switches. We prove that the proposed limiters provide true limiting by clamping the transmitted intensity at a level which is independent of the incident intensity. We explore the response of optical switches for signal and pump beams having the same and different frequencies. We describe and quantify the performance of the proposed structures in the realization of all-optical OR gates and optical hard-limiters. In addition, we prove that, for fabrication errors as large as 10%, qualitative device functionality remains, with performance only modestly degraded.