Doubt 1:
CFL $\cap$ DCFL = CFL
CFL – Context Free Languages
DCFL – Deterministic Context Free Languages
Can you prove above expression
Doubt 2:
Consider L$_{1}$ = Language generated by a machine M1
L$_{2}$ = Language generated by a machine M2
Machine can be – FA, PDA, LBA, or TM
Assuming Machine M2 is more powerful than M1
Let L$_{3}$ = L$_{1}$ $\cap$ L$_{2}$
Now can we say that L$_{3}$ can be generated by Machine M2
For eg:
L1 = Context Free Language (i.e Generated by NPDA)
L2 = Recursively enumerable language (i.e Generated by TM)
Now can we say L$_{1}$ $\cap$ L$_{2}$ is Recursively Enumerable Language i.e it can be generated by a TM
Doubt 3:
Non Recursively Enumerable Language $\cap$ Any language = Non Recursively Enumerable Language
Is this statement correct/always true?