I'm looking for various researches which consider specific subclasses of Context-Free Grammar class, i.e. some specific described cases, which differ from well-known:
- deterministic/non-deterministic
- ambiguous/unambiguous
- regular/non-regular
As an example of such "non-standard" subclasses are Visibly pushdown grammar described here. Any additional examples will be much appreciated.
More specifically, I'm wondering, are any described subclasses which can help distinguish this two very similar cases?
$G_1$:
$S\rightarrow aD$, $S\rightarrow cD$
$D\rightarrow abc$, $D\rightarrow abDc$
$G_2$:
$S\rightarrow aD$, $S\rightarrow cD$
$D\rightarrow abc$, $D\rightarrow abDc$, $D\rightarrow aDb$, $D\rightarrow aDc$
It is clear that both of them are unambiguous non-determ. CFG, and $\mathcal{L}(G_1)\subset\mathcal{L}(G_2)$. But these are common properties, I'm looking for specific differences.