My MA final project at Stony Brook University focused on some of the computational requirements of carrying out sideward movement using tree automata. More formally, it explored the idea that multi-bottom-up tree transducers are able to handle many ordinary types of syntactic movement, but there are some inherent properties of sideward movement that require something much more computationally robust. So if we take a sideward movement analysis of some syntactic phenomenon, be it parasitic gaps, pseudo-gapping, adjunct control, etc. then this phenomenon must be more computationally complex than say wh-movement. This may not be a particularly surprising claim on its own, but having the mathematical vocabulary to motivate and justify that fact is the cool part in my opinion. I think this is a pretty neat example of how some seemingly unrelated concept used in theoretical computer science (tree walking pebble automata used in XML/database theory) can be applied to solving a problem in natural language syntax!