Anssi Yli-Jyrä

• Nested complementation plays an important role in expressing counter- i.e. star-free and first-order definable languages and their hierarchies. In addition, methods that compile phonological rules into finite-state networks use double-nested complementation or “double negation”. This paper reviews how the double-nested complementation extends to a relatively new operation, generalized restriction (GR), coined by the author (Yli-Jyrä and Koskenniemi 2004). This operation encapsulates a double-nested complementation and elimination of a concatenation marker, diamond, whose finite occurrences align concatenations in the arguments of the operation. The paper demonstrates that the GR operation has an interesting potential in expressing regular languages, various kinds of grammars, bimorphisms and relations. This motivates a further study of optimized implementation of the operator.