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The paper introduces novel field programmable gate array (FPGA) circuits based on hybrid CMOS/resistive switching device (memristor) technology and explores several logic architectures. The novel FPGA structure is based on the combination of CMOL (Cmos + MOLecular scale devices) FPGA circuits and recent improvements and generalization of the CMOL concept to allow multilayer crossbar integration, compatibility with state-of-the-art foundries, and a wide range of available memristive crosspoint devices. Preliminary results indicate that with no optimization and only conventional CMOS technology, the proposed circuits can be at least ten times denser (and potentially faster) than CMOS FPGAs with the same design rules and similar power density. The second part of this paper shows that this performance can be further improved using optimal MUX-based logic architecture.