Automata, Complexity, and Optimality Theory

Bob Frank, Giorgio Satta, and Lauri Karttunen stunned the computational OT community some years ago when they pointed out that unidirectional optimization is essentially a finite state technique. If all components of an OT system can be modeled by a finite state machine, then the complexity of the entire system does not exceed the complexity of its components. There has been some debate in past years whether simple unidirectional optimization should be complemented by some component of “recoverability”, which led to various notions of bidirectional optimization. The most radical of these proposals, Blutner’s “Weak Bidirectionality”, is in fact computationally more complex than all other proposed evaluation methods because it introduces an element of recursion. Recent work by Christian Wartena, Stephan Kepser and Uwe Mönnich shows that the complexity landscape for finite state OT is almost identicallly replicated at the level of tree automata. This class of automata is considerably more expressive than finite state string automata. Therefore the new results promise to be relevant for the working OT syntactician/semanticist. After a recapitulation of previous work on the automata theoretic complexity of unidirectional and bidirectional OT, the paper explores the implementability of bidirectional OT with finite state tree automata.