That is just laughable, Norway banned spay and neutering and they don't have an overpopulation/stray problem. It's not a dog problem, it's a people problem. Responsible dog owners don't let their dogs roam free. The US is full of irresponsible retards that don't know how to care for/train animals or just don't care. The fact that the US still has an overpopulation of strays is indicative that the spay and neuter crusade that's been going on for decades here just can't fix stupid and will never address the real issue.
And for legal purposes, your sign should just state "Dog on Premises"