According to the label, Roundup is safe for pets and children to walk on as soon as it dries completely. Monsanto doesn't suggest this for the safety of their pets, but rather to prevent pets from tracking wet Roundup to other areas of lawns or flower beds. Roundup's moist waste can harm your plants and pets. It can be difficult to determine exactly how long pets should stay away after spraying an herbicide.
However, 30 hours is the minimum time to ensure they are completely safe. Patio size and temperature also play an important role in determining temperature. Most herbicides or pesticides usually include this information on their label. Otherwise, you should be careful not to let your dog run across the grass until it's completely dry.
If your herbicide contains chemicals, the answer is no. Many over-the-counter herbicides contain glyphosate, a herbicide that has been linked to cancer in both humans and dogs. The most popular weed spray contains the isopropylamine salt of glyphosate.