# Transductions of context-free languages into sets of sentential forms

## Abstract

Divide the context-free languages into equivalence classes in the following way: L_{1} and L_{2} are in the same class if there are a-transducers M and \(\bar M\)such that M(L_{1})=L_{2} and \(\bar M\)(L_{2})=L_{1}. Define L_{1} and L_{2} to be structurally similar if they are in the same class. Among the results given below are: 1) if L_{1} and L_{2} are structurally similar and L_{1} has a structurally similar set of (right) sentential forms then so does L_{2}, 2) if L_{1} and L_{2} are structurally similar and L_{1} is deterministic then L_{2} has a structurally similar set of right sentential forms, 3) if L_{1} and L_{2} are structurally similar and L_{1} is a parenthesis language then L_{2} has a structurally similar set of sentential forms, 4) there is a nonempty equivalence class of structurally similar languages that contains no (right) sentential forms of any grammar, 5) if an equivalence class contains any set of (right) sentential forms at all then every language in the class has a set of (right) sentential forms in that class.

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