Local Group dwarf galaxies and the star formation law at high redshift

I show how the existing observational data on Local Group dwarf galaxies can be used to estimate the average star formation law during the first 3 Gyr of the history of the universe. I find that the observational data are consistent with the orthodox Schmidt law with a star formation efficiency of about 4% if the star formation is continuous (during the first 3 Gyr). The efficiency is proportionally higher if most of the gas in the dwarfs was consumed (and never replenished) in a short time interval well before the universe turned 3 Gyr.