Here is a collection of industry papers.

These document provide extremely useful information about the viability and credibility regarding the on board electrolysis of water and their results.

1. International Journal of Hydrogen Energy (a respected, peer-reviewed journal) published a paper by Dulger & Ozcelik entitled “Fuel economy improvement by on board electrolytic hydrogen production”, in which they found that the production of hydrogen on-the-fly was able to increase fuel economy by 35-40% and reduce emissions by 40-50% in four carburetted vehicles (attached).  Obviously this is only possible if the engine is not making full use of the energy of the fuel it is supplied with, e.g. due to a slow burn (hydrogen combusts at an extremely high speed, making any fuel it is mixed with also burn faster).