Learning Left-to-Right and Right-to-Left Iterative Languages

The left-to-right and right-to-left iterative languages are previously unnoticed subclasses of the regular languages of infinite size that are identifiable in the limit from positive data. Essentially, these language classes are the ones obtained by merging final states in a prefix tree and initial states in a suffix tree of the observed sample, respectively. Strikingly, these classes are also transparently related to the zero-reversible languages because some algorithms that learn them differ minimally from the ZR algorithm given in Angluin (1982). Second, they are part of the answer to the challenge provided by Muggleton (1990), who proposed mapping the space of language classes obtainable by a general statemerging algorithm IM1. Third, these classes are relevant to a hypothesis of how children can acquire sound patterns of their language—in particular, the hypothesis that all phonotactic patterns found in natural language are neighborhood-distinct (Heinz 2007).