Prove that all regular languages are context free. Note: Proof must proceed by structural induction on...

Prove that all regular languages are context free.

Note: Proof must proceed by structural induction on regular expressions

Please prove by Structural Induction. Will Upvote for correct answer. Thanks

Expert Solution

The proof using structural induction on the number of operators of a Regular Language is sketched below in the pictures.The Solution first explains what Structural Induction is and then proceeds with the proof.

venereology answered 1 year ago

Regular => Context-Free Give a proof by induction on regular expressions that: For any language A,...

Regular => Context-Free Give a proof by induction on regular expressions that: For any language A, if A is regular, then A is also context-free. You may assume that the statements from the previous Closure under Context-Free Languages problem are proved. R is a regular expression if RR is: a for some a∈alphabet Σ, the empty string ε, the empty set ∅, R1∪R2, sometimes written R1∣R2, where R1 and R2 are regular expressions, R1∘R2, sometimes written R1R2, where R1 and...

5 Regular => Context-Free Give a proof by induction on regular expressions that: For any language...

5 Regular => Context-Free Give a proof by induction on regular expressions that: For any language A, if A is regular, then A is also context-free. You may assume that the statements from the previous Closure under Context-Free Languages problem are proved.

Prove the following Closure Properties with respect to Context Free Languages. 1. Show that Context Free...

Prove the following Closure Properties with respect to Context Free Languages. 1. Show that Context Free Languages are Closed under union(∪), concatenation(·), kleene star(*). (Hint: If L1 and L2 are Context Free languages then write Context Free grammar equivalent to L1 ∪ L2, L1 · L2, L∗ 1 ) 2. Show that if L1 and L2 are Context Free Languages, then L1 ∩ L2 is not necessarily Context Free. (Hint: Use Proof by Counter Example)

Prove that the proof by mathematical induction and the proof by strong induction are equivalent

(a) How Context Free languages are different from Regular languages. (b) What are the automata accepting...

(a) How Context Free languages are different from Regular languages. (b) What are the automata accepting those languages and how they are different from DFA and NFA. (c) How the grammar of Context Free Languages looks different from those in Regular languages.

Please be able to follow the COMMENT Use induction proof to prove that For all positive...

Please be able to follow the COMMENT Use induction proof to prove that For all positive integers n we have the inequality n<=2^n here is the step: base step: P(1)= 1<=2^1 inductive step: k+1<= 2^(k)+1 <= 2^(k)+k (since k>=1) <= 2^(k)+2^(k) = 2X2^(k) =2^(k+1) i don't understand why 1 can be replaced by k and i don't know why since k>=1

Are the following languages over {a, b} regular? If they are then prove it. If they...

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Closure under Context-Free Languages Show that the following operations are closed under context-free languages: union concatentation...

Closure under Context-Free Languages Show that the following operations are closed under context-free languages: union concatentation Kleene star

Prove whether the following are regular (include the file) or not regular (attach a proof). The...

Prove whether the following are regular (include the file) or not regular (attach a proof). The alphabet is {0, 1}. 1. The set of strings that start with N 0's which are directly followed by 2N 1's. 2. The set of strings start with two 0's, followed by N 1's, followed by N 1's and end with three 0's. 3. The set of strings where every substring of length 5 has more 0's than 1's. Strings less than length five...

Course: Discrete Math Show/Prove that the principal of strong induction and regular induction are equivalent.

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