Long words in maximum entropy phonotactic grammars

A phonotactic grammar assigns a well-formedness score to all possible surface forms. This paper considers whether phonotactic grammars should be probabilistic, and gives several arguments that they need to be. Hayes & Wilson (2008) demonstrate the promise of a maximum entropy Harmonic Grammar as a probabilistic phonotactic grammar. This paper points out a theoretical issue with maxent phonotactic grammars: they are not guaranteed to assign a well-defined probability distribution, because sequences that contain arbitrary repetitions of unmarked sequences may be underpenalised. The paper motivates a solution to this issue: include a *STRUCT constraint. A mathematical proof of necessary and sufficient conditions to avoid the underpenalisation problem are given in online supplementary materials.