| Property | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| Reversal | + | + | + | + |
| Concatenation | + | + | + | + |
| Intersection with Regular Sets | + | + | + | + |
| Union | + | + | + | + |
| Intersection | - | + | - | + |
| Complement | - | + | - | + |
| Concatenation | + | + | + | + |
| L(G) Empty? | - | - | + | + |
| L(G) Finite? | - | - | + | + |
| L(G) Infinite? | - | - | + | + |
| L1 ≡ L2? | - | - | - | + |
| L1 ⊆ L2? | - | - | - | + |
| L(G) = Σ*? | - | - | - | + |
| S ⇒ x for some x? | - | + | + | + |
| S ⇒ w x y for some x? | - | - | + | + |
| Ambiguous? | - | - | - | + |
| Arbitrary language of this type? | - | - | - | - |
| ∃ an equivalent unambiguous grammar? | + | - | + | |
| λ in L(G)? | + | + | + | |
| L(G) = {λ}? | + | + |