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Relevant information in positron emission tomography is currently being obtained mostly by analog signal-processing methods. New digital PET scanner architectures are now becoming available, which offer greater flexibility and easier reconfiguration capability as compared to previous PET designs. Moreover, new strategies can be devised to extract more information with better accuracy from the digitized detector signals. Trained artificial neural networks (ANN) have been investigated to improve coincidence timing resolution with different types of Avalanche PhotoDiode (APD)-based detectors. The signal at the output of a charge-sensitive preamplifier was digitized with an off-the-shelf, free-running 100-MHz, 8-bit analog-to-digital converter and time discrimination was performed with ANNs implemented in field-programmable gate array (FPGA). Results show that ANNs can be particularly efficient with slow and low light output scintillators, such as BGO, but less so with faster luminous crystals, such as LSO. In reference to a fast PMT-plastic detector, a time resolution of 6.5 ns was achieved with a BGO-APD detector. With LSO, the ANN was found to be competitive with other digital techniques developed in previous works. ANNs implemented in FPGAs provide a fast and flexible circuit that can be easily reconfigured to accommodate various detectors under different signal/noise conditions.