Summary
The concept of inverse well-known for homomorphisms and gsm-mappings is extended to any language operation. The class IRP of language operations whose inverse preserves regularity is considered. As an application a necessary and sufficient condition is established for the class of relations recognizable by finite automata to be closed under different versions of bounded quantification.
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Laurinolli, T. Bounded quantification and relations recognizable by finite automata. Acta Informatica 10, 67–78 (1978). https://doi.org/10.1007/BF00260924
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DOI: https://doi.org/10.1007/BF00260924