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Is the union of two context free languages context-free?
Note: Context-free languages are closed under union operation, so union of two CFLs are always CFL (that can be regular as class of regular languages is subset of class of CFLs), but it can’t be a non-CFL e.g. CSL.
Is context free language closed under union?
Context-free languages are not closed under complementation. L1 and L2 are CFL. Then, since CFLs closed under union, L1 ∪ L2 is CFL.
Is it true that a union of a deterministic context free language with a regular language is deterministic context-free How about intersection justify your answers?
Yes, deterministic context-free languages are closed under union with regular languages. It is easy to show they are closed under intersection with regular languages.
Which of the following can be used to prove that a language is not context free?
Which of the following can be used to prove a language is not context free? Explanation: We can use the properties of regular closure to prove that a language is not a context free language. Example: Intersection of context free language and regular language is a context free language.
Is L1 L2 context free?
Option (C) says L1, L2 and L3 are context free. L3 languages contains all strings with n no.
Which of the following can be used to prove that a language is not context-free?
Is L1 ∩ L2 is a context-free language?
Intersection − If L1 and L2 are context free languages, then L1 ∩ L2 is not necessarily context free. Intersection with Regular Language − If L1 is a regular language and L2 is a context free language, then L1 ∩ L2 is a context free language.
Which of the statement is true if L1 & L2 are context-free language?
Explanation: Given L1 is a context free language and L2 as a regular language then L1-L2 is context free language and ~L1(complement of context free) is not context free because context free is not closed under complement.
What is a context free language?
Context Free languages are accepted by pushdown automata but not by finite automata. Context free languages can be generated by context free grammar which has the form : Union : If L1 and If L2 are two context free languages, their union L1 ∪ L2 will also be context free. For example,
Is L1 context free or not?
Similarly, complementation of context free language L1 which is ∑* – L1, need not be context free. Note : So CFL are not closed under Intersection and Complementation. Deterministic CFL are subset of CFL which can be recognized by Deterministic PDA.
What is context free in Kleene closure?
Kleene Closure : If L1 is context free, its Kleene closure L1* will also be context free. For example, L1* = { a n b n | n >= 0 }* is also context free. Note : So CFL are closed under Kleen Closure. Intersection and complementation : If L1 and If L2 are two context free languages, their intersection L1 ∩ L2 need not be context free.
Is concatenation L1 and L2 context free?
Concatenation : If L1 and If L2 are two context free languages, their concatenation L1.L2 will also be context free. For example, L3 = L1.L2 = { a n b n c m d m | m >= 0 and n >= 0} is also context free.