Optimality Theory and Vector Semirings

As [1] and [2] have shown, some applications of Optimality Theory can be modelled using finite state algebra provided that the constraints are regular. However, their approaches suffered from an upper bound on the number of constraint violations. We present a method to construct finite state transducers which can handle an arbitrary number of constraint violations using a variant of the tropical semiring as its weighting structure. In general, any Optimality Theory system whose constraints can be represented by regular relations, can be modelled this way. Unlike [3], who used roughly the same idea, we can show, that this can be achieved by using only the standard (weighted) automaton algebra.