This question can look like some kind of puzzle, but it is actually part of more complex applied problem.
Let's consider subspace of Context-Sensitive Grammars, which contains grammars which can not be represented neither as Context-Free Grammars, neither as Regular Grammars. Let's call them "strong CSG".
And let's suppose that we are given only by alphabet, set of nonterminals, set of production rules, but without left sides (which is hidden from us). For instance:
- $?\rightarrow abc$
- $?\rightarrow aSBc$
- $?\rightarrow WB$
- $?\rightarrow WX$
- $?\rightarrow BX$
- $?\rightarrow Bc$
- $?\rightarrow bb$
The question is: are any general properties regarding right-side of these production rules using which we can distinguish strong-CSG from CFG and RG looking only on this non-complete set of rules?
Alternative formulation of this question: in this particular case, can given grammar be Context-free?
Let's also consider that in case of CFG given grammar is always present in reduced (simplified) form (by reduction I mean finding a CFG with the fewest nonterminal symbols or with the fewest rules that is equivalent to G) - (we're talking here about weak-equivalent grammar with smallest number of non-terminals and production rules - thanks to @Marzio De Biasi for pointing this).
Disclaimer: original grammar was Context-Sensitive, taken from wikipedia article.