Prevention measures can really help. Regularly brush the slabs with a good stiff broom to remove dirt and/or debris and starting young moss. This can help tremendously if it is done consistently.
Another prevention measure, if you can add sunlight by trimming overhead branches that can help significantly. Any drainage improvements to remove moisture helps.
A pressure washer will blast away moss and dirt and can be used without chemicals but must be used cautiously to protect valued tiny plants.
Vinegar and water as recommended by
@oneeye is effective.