Arjun Suresh (talk | contribs) (→For CFGs G, G1 and G2 and regular set R) |
Arjun Suresh (talk | contribs) (→For CFGs G, G1 and G2 and regular set R) |
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===For CFGs G, G1 and G2 and regular set R=== | ===For CFGs G, G1 and G2 and regular set R=== | ||
+ | The following problems are undecidable: | ||
− | + | # <math>(L(G1))^\complement</math> is a CFL | |
− | + | # L(G1) \cap L(G2) is a CFL | |
− | + | # L(G1) \cap L(G2) is empty | |
− | + | # L(G1) = R | |
− | + | # Whether G is ambiguous |
Grammar | <math>w \in L(G)</math> | <math>L(G) = \phi</math> | <math>L(G) = \Sigma^*</math> | <math>L(G_1) \subseteq L(G_2)</math> | <math>L(G_1) = L(G_2)</math> | <math>L(G_1) \cap L(G_2) = \phi</math> | <math>L(G) is finite</math> |
---|---|---|---|---|---|---|---|
Regular Grammar | D | D | D | D | D | D | D |
Det. Context Free | D | D | D | UD | ? | UD | D |
Context Free | D | D | UD | UD | UD | UD | D |
Context Sensitive | D | UD | UD | UD | UD | UD | UD |
Recursive | D | UD | UD | UD | UD | UD | UD |
Recursively Enumerable | D | UD | UD | UD | UD | UD | UD |
The following problems are undecidable:
Grammar | <math>w \in L(G)</math> | <math>L(G) = \phi</math> | <math>L(G) = \Sigma^*</math> | <math>L(G_1) \subseteq L(G_2)</math> | <math>L(G_1) = L(G_2)</math> | <math>L(G_1) \cap L(G_2) = \phi</math> | <math>L(G) is finite</math> |
---|---|---|---|---|---|---|---|
Regular Grammar | D | D | D | D | D | D | D |
Det. Context Free | D | D | D | UD | ? | UD | D |
Context Free | D | D | UD | UD | UD | UD | D |
Context Sensitive | D | UD | UD | UD | UD | UD | UD |
Recursive | D | UD | UD | UD | UD | UD | UD |
Recursively Enumerable | D | UD | UD | UD | UD | UD | UD |
1.) the compliment of <math>(L(G1))^\complement</math> is a CFL
2.) L(G1) intersected with L(G2) is a CFL 3.) L(G1) = R
It is undecidable whether an arbitrary CFG is ambiguous
It is undecidable for arbitrary CFG's G1 and G2 whether L(G1) intersected with L(G2) is empty