Can condo association or HOA ban dogs?

Can a pet-friendly condo building pass a rule that does not allow renters to have pets? Our building is nearly up to 33% renters and almost all of the renters have dogs. Many owners have dogs as well, but with the higher renting rate, there has been a significant increase in dog messes in the common areas (elevator and hallways). I can't believe it is the owners not cleaning up after themselves, but rather it's the renters.