Structural Equivalence and ET0L Grammars

For a given context-sensitive grammar G we construct ET0L grammars G1 and G2 that are structurally equivalent if and only if the language generated by G is empty, which implies that structural equivalence is undecidable for ET0L grammars. This is in contrast to the decidability result for the E0L case. In fact, we show that structural equivalence is undecidable for propagating ET0L grammars even when the number of tables is restricted to be at most two. A stronger notion of equivalence that requires the sets of syntax trees to be isomorphic is shown to be decidable for ET0L grammars.

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