Cat hating dog

[happygardening]

One of my dogs used to live with what can only be described as an alpha cat. He completely ruled the roost and the dog was frankly terrified of him. The cat could go where ever he wanted sleep where ever he wanted eat what ever he and god help any dog or even human who got in his way. The large scar across the dogs nose is a permanent reminder of what happened if you crossed him. Four years ago he was very sadly run over (dog smirks).
We now own a normal cat whose slightly cautious of dogs and the dog has decided "never again am I giving up the best seat/food/place in the sun to a bloody cat." So when ever he sees him he growls and leaps at him the cat then runs away This is currently okay becasue they have live in different parts of the house and are separated by a stair gate. But all this is about to change when I'm at home it will no longer be possible to separate them I actually don't think the dog would harm the cat he's all mouth but I think he's going to make the cat exceedingly anxious and unhappy.
Any ideas?