Again.....
Look, there's something like energy summary. It means that energy needed to get oxygen and hydogen from the water (electrolysis) is far more that you will get from burning them. The simplest example (followed in teh whole nature, and called entropia) - will you spend more energy making order in your room, or making mess? 
It CANNOT work. The physics that we know, doesn't permit it.
Your driving the generator no matter what.
I don't know much about the physics/chemistry or thermodynamics (but, I can spell it

)
Most of the 'things' on internet a present use lower than atmospheric pressure low voltage electrolysis, in effect they are water vapor/hydrogen (running a 'steam engine

)
The water vapor expands more than air and also cools cylinder. (same reasoning that bikes run better when its foggy out)
From the research I've done over last several years it only needs 1.5~2% of 'Browns Gas' to allow a leaner mixture burn. Hydrogen has an octane rating around 130 but burns much faster than gasoline so timing etc has to be modified.
Engine has to be running at relatively high rpm for most of the stuff to work (ign at full advance, 3,000rpm or more)
There is an awful lot of nonsense being put about at present with some downright lies about mpg improvements. (going from 25 mpg to 80+mpg aint gonna happen) Best you can realistically hope for is 2~3% or about what you lose by using 10% ethanol gas
Just my 2 cents
PJ