Line 10: Line 10:
 
! <math>L(G_1) \cap L(G_2) = \phi</math>
 
! <math>L(G_1) \cap L(G_2) = \phi</math>
 
|-
 
|-
|Regular
+
|Regular Grammar
| {{Yes}}
+
| {{D}}
| {{Yes}}
+
| {{D}}
| {{Yes}}
+
| {{D}}
| {{Yes}}
+
| {{D}}
| {{Yes}}
+
| {{D}}
| {{Yes}}
+
| {{D}}
 
|-
 
|-
|DCFG
+
|Det. Context Free
| {{Yes}}
+
| {{D}}
| {{Yes}}
+
| {{D}}
| {{No}}
+
| {{UD}}
| {{No}}
+
| {{UD}}
 
| {{?}}
 
| {{?}}
| {{No}}
+
| {{UD}}
 
|-
 
|-
|Complement
+
|Context Free
| {{Yes}}
+
| {{D}}
| {{Yes}}
+
| {{D}}
| {{No}}
+
| {{UD}}
| {{Yes}}
+
| {{UD}}
| {{Yes}}
+
| {{UD}}
| {{No}}
+
| {{UD}}
 
|-
 
|-
|Concatenation
+
|Context Sensitive
| {{Yes}}
+
| {{D}}
| {{No}}
+
| {{UD}}
| {{Yes}}
+
| {{UD}}
| {{Yes}}
+
| {{UD}}
| {{Yes}}
+
| {{UD}}
| {{Yes}}
+
| {{UD}}
 
|-
 
|-
|Kleene star
+
|Recursive
| {{Yes}}
+
| {{D}}
| {{No}}
+
| {{UD}}
| {{Yes}}
+
| {{UD}}
| {{Yes}}
+
| {{UD}}
| {{Yes}}
+
| {{UD}}
| {{Yes}}
+
| {{UD}}
|-
 
|Homomorphism
 
| {{Yes}}
 
| {{No}}
 
| {{Yes}}
 
| {{No}}
 
| {{No}}
 
| {{Yes}}
 
|-
 
|<math>\epsilon</math>-free Homomorphism
 
| {{Yes}}
 
| {{No}}
 
| {{Yes}}
 
| {{Yes}}
 
| {{Yes}}
 
| {{Yes}}
 
|-
 
|Substitution (<math>\epsilon</math>-free)
 
| {{Yes}}
 
| {{No}}
 
| {{Yes}}
 
| {{Yes}}
 
| {{No}}
 
| {{Yes}}
 
|-
 
|Inverse Homomorphism
 
| {{Yes}}
 
| {{Yes}}
 
| {{Yes}}
 
| {{Yes}}
 
| {{Yes}}
 
| {{Yes}}
 
|-
 
|Reverse
 
| {{Yes}}
 
| {{No}}
 
| {{Yes}}
 
| {{Yes}}
 
| {{Yes}}
 
| {{Yes}}
 
 
|-
 
|-
 +
|Recursively Enumerable
 +
| {{D}}
 +
| {{UD}}
 +
| {{UD}}
 +
| {{UD}}
 +
| {{UD}}
 +
| {{UD}}
 +
 
|}
 
|}

Revision as of 18:06, 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>
Regular Grammar D D D D D D
Det. Context Free D D UD UD ? UD
Context Free D D UD UD UD UD
Context Sensitive D UD UD UD UD UD
Recursive D UD UD UD UD UD
Recursively Enumerable D UD UD UD UD UD
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>
Regular Grammar D D D D D D
Det. Context Free D D UD UD ? UD
Context Free D D UD UD UD UD
Context Sensitive D UD UD UD UD UD
Recursive D UD UD UD UD UD
Recursively Enumerable D UD UD UD UD UD