I've solved the roaming-neighborhood/stray cat-in-my-yard issue by training my dog to "get the kitty!" She chases them like gangbusters right to the edge of the yard. When we got the chickens, she wanted to eat them, but since we've had them for a couple of weeks, she now realizes they are part of the family and will sit near their coop facing outward, challenging any predatory intruders who dare to pass...so cute!