Compiling contextual restrictions on strings into finite-state automata

The paper discusses a language operation that we call context restriction. This operation is closely associated with context restriction rules (Kosken- niemi, 1983; Kiraz, 2000), right-arrow rules or implication rules (Kosken- niemi et al., 1992; Voutilainen, 1997) and the restriction operator (Beesley and Karttunen, 2003). The operation has been used in finite-state phonology and morphology in certain limited ways. A more general setting involves re- stricting overlapping occurrences of a center language under context condi- tions. Recently, star-free regular languages (and all regular languages) have been shown to be closed under context restrictions with such “overlapping centers” (Yli-Jyra ̈, 2003), but the construction involved is overly complex and becomes impractical when the number of operands grows.
In this paper, we improve this recent result by presenting a more practical construction. This construction is not only simpler but it also leads to a generalization where contexts and centers may appear as conditions at both sides of the implication arrow (⇒): licensing conditions on the right-hand side specify the restriction and triggering conditions on the left-hand side regulate activation of the restriction. One application of the generalization is to facilitate splitting certain context restriction rules in grammars into a conjunction of separate rules.