Transductions of context-free languages into sets of sentential forms
Divide the context-free languages into equivalence classes in the following way: L1 and L2 are in the same class if there are a-transducers M and \(\bar M\)such that M(L1)=L2 and \(\bar M\)(L2)=L1. Define L1 and L2 to be structurally similar if they are in the same class. Among the results given below are: 1) if L1 and L2 are structurally similar and L1 has a structurally similar set of (right) sentential forms then so does L2, 2) if L1 and L2 are structurally similar and L1 is deterministic then L2 has a structurally similar set of right sentential forms, 3) if L1 and L2 are structurally similar and L1 is a parenthesis language then L2 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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