Are large dogs permitted if they are certified service dogs

But you need to keep your pets off the street without supervision. Otherwise animal control may be called to remove unsupervised pets

Yes, people have pets..they don't have to be service dog's .

Service dogs are allowed

Certified service pets are allowed, but strictly on a leash. I don't think that the size matters, but if the dog gets out a few times on his own you could have problems with the HOA forcing you to keep the animal indoors and possibly find.