Is There a Relationship Between Model Checking and Browser Testing?

This reminds me a bit of what model checking people are doing, sort of also exploring the state of a model. So it really is more like property based testing, in that sense,. You have a very, not necessarily a very limited but a more limited exploration of the state space. Can you do anything to speed up it? Because I can imagine that you don't want to parse the DOM after every state change or that you might want to recognize when you're in a state that you've seen previously.