Difference between revisions of "Grammar: Decidable and Undecidable Problems"

Revision as of 18:29, 26 February 2014

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) 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

Other Undecidable Problems

For CFGs G, G1 and G2 and regular set R

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