Grammar: Decidable and Undecidable Problems Revision as of 18:50, 26 February 2014 by Arjun Suresh (talk | contribs) (→‎For arbitrary CFGs G, G1 and G2 and an arbitrary regular set R) (diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Grammar: Decidable and Undecidable Problems

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)</math> is finite
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

Other Undecidable Problems

For arbitrary CFGs G, G1 and G2 and an arbitrary regular set R

The following problems are undecidable:

1. Whether <math>(L(G1))^\complement</math> is a CFL
2. Whether <math>L(G1) \cap L(G2)</math> is a CFL
3. Whether <math>L(G1) \cap L(G2)</math> is empty
4. Whether <math>L(G) = R</math>
5. Whether <math>L(G) \subseteq R</math>
6. Whether <math>R \subseteq L(G)</math>
7. Whether <math>G</math> is ambiguous
8. Whether <math>L(G)</math> is DCFL

Whether <math>R \subseteq L(G)</math> is decidable