Although it's neither an alga nor a moss, an algae and moss-killing herbicide might be effective, but you would have to see if Nostoc is listed on the label, or ask the manufacturer if it works on that organism. Herbicide active ingredient options may include potassium salts of fatty acids or pelargonic acid, the latter of which might damage other plants if it comes into direct contact with them. As the linked page notes, this is not a complete solution because, while it may kill existing Nostoc, it won't keep it from coming back if the conditions supporting its growth are not addressed.

Nostoc thrives in areas with poor drainage and a bit of nutrient availability, so perhaps organic debris (maybe from nearby tree leaves that land on the roof and disintegrate) is building up between the stone, as it can on the ground in nurseries and similar locations. Since the roof is flat, it might not be easy to improve its drainage, but that could be something you could ask a structural engineer about. Even if there was a type of herbicide that could be applied almost like a pre-emergent to prevent Nostoc regrowth or colonization of the roof, its use would be discouraged over non-chemical prevention methods since residues running off in stormwater could potentially pollute surface or ground water or impact the surrounding landscape. Physical removal of the Nostoc is the most immediate approach, though admittedly more tedious and not foolproof, since pieces left behind could regrow.

Miri

Thank you, and you're welcome!