Neural logic blocks (NLBs) enable the realization of biologically inspired reconfigurable hardware. Networks of NLBs can be trained to perform complex computations such as multilevel Boolean logic and optical character recognition (OCR) in an area- and energy-efficient manner. Recently, several groups have proposed perceptron-based NLB designs with thin-film memristor synapses. These designs are implemented using a static threshold activation function, limiting the set of learnable functions to be linearly separable. In this work, we propose two NLB designs-robust adaptive NLB (RANLB) and multithreshold NLB (MTNLB)-which overcome this limitation by allowing the effective activation function to be adapted during the training process. Consequently, both designs enable any logic function to be implemented in a single-layer NLB network. The proposed NLBs are designed, simulated, and trained to implement ISCAS-85 benchmark circuits, as well as OCR. The MTNLB achieves 90 percent improvement in the energy delay product (EDP) over lookup table (LUT)-based implementations of the ISCAS-85 benchmarks and up to a 99 percent improvement over a previous NLB implementation. As a compromise, the RANLB provides a smaller EDP improvement, but has an average training time of only ≈ 4 cycles for 4-input logic functions, compared to the MTNLBs ≈ 8-cycle average training time.