|Title:||Quadratic Alignment Constraints and Finite State Optimality Theory|
|Comment:||first page is a cover page containing information on the paper itself|
|Abstract:||The maximal number of violation marks that an input string (e.g. a word) can be assigned is 1) constant for some constraints, 2) proportional to the length of the word for others,or 3) can grow faster than the length of the word for non-linear (e.g. quadratic) constraints. Gradient constraints that can be reformulated as non-gradient belong to the first two types, while ``inherently'' gradient constraints may be non-linear.
The following paper applies this typology to alignment constraints used for metrical stress assignment: ALIGN(Word,Foot) belongs to the first category, ALIGN(Main-foot,Word) is linear. While ALIGN(Foot,Word)
is quadratic, thus non-linear.
Furthermore, it has been claimed since the 1970s that a major part of phonology has actually a generative power not stronger than a regular grammar (i.e. a finite state automaton). Can OT be realized as a finite state transducer? In this paper we shall prove that non-linear constraints cannot be encoded using finite state tools, thus OT systems including such constraints cannot be realized this way.
This fact can support McCarthy's recent arguments against gradience.