Find a context-free grammar for each of the following languages over the alphabet {a, b}. (N: the natural number set) a. {anb2n | n ∈ N U {0}} U {an+2bn | n ∈ N} b. {ambn | m, n ∈ N, and n > m}.

Q: Provide the rules for context-free grammars that generate the following languages. L5 = {aibjck |…

A: Context-free grammars are formal systems used to describe languages in a structured manner. In this…

Q: Let L be the language [a^i b^2i a^i | i >0}. a) Construct a context-sensitive grammar G that…

A:

Q: (g) L = {w|w| mod 3 = 0, w ‡ 5}.

A: The language L consists of all strings over the alphabet {a, b} that have a length that is divisible…

Q: Q2: B/ Construction string of the language of a minimal DFA accepting a se contains 'ab' as the…

A: Given :

Q: Consider the language L generated by the following grammars G, S→AB | AA; A→BB | a; B→AB | b. Use…

A: Given grammar is, S->AB | AA A->BB | a B->AB | b Given string is: w= "babab"

Q: For each of the languages below, determine whether the language is regular or not. If the language…

A: Here is the solution:-

Q: Given: Language L2 = {w ϵ {a,b}* | w contains substring aab} Construct the DFA representing the…

A: Solution:

Q: 4. Consider the following languages. • ANFAFIN = {(N) |N is an NFA and L(N) is finite} • EREX = {(R)…

A: Answer:- No,All strings of the form 10n are contained in L(N) (in addition to other strings as…

Q: Construct an npda that accepts the regular language L (aaa*b).

A: construct an nondeterministic push-down automata  L(aaa*b)

Q: Consider the following grammar: S → O U U → + S | ε O →  ( S ) | int G G →  * O | ε Show the…

A: Instructions: Initialize the stack with the starting terminal and put a “$” symbol. In the input…

Q: For each of the following languages Ls {a, b}*, show that the elements of the infinite set {a"|n >…

A: Shown that the given language is pairwise distinguishable

Q: Rewrite BNF to EBNF BNF: Кеxpr> -→ + | - | → * | / | → ** → () |id

A: According to the information given:- We have to convert BNF to EBNF.

Q: The following grammar G generates numbers in binary notation. C --> C 0 | A 1 |0 (C is the start…

A: Proved the given languages equivalent

Q: (a) Construct context-free grammars that generate the following languages. (i) The language of all…

A: In questions with many parts, we must answer the unrelated first one.

Q: 2- Construct a RE over E={0,1} such that It does not contain any string with two consecutive "O"s It…

A: Solution:- 2- Construct a RE over E={0,1}   ​​​​​​1) It does not contain any string with two…

Q: 9. Given the regular expression r = a(a+b)*b a) Show an nfa that accepts the language L(r) b) Show…

A: A regular expression is a sequence of characters that represents a pattern. It is a powerful tool…

Q: Let G = (V. E, P, S) be a context-free grammar in which SS only when n = 0. G is an LR(k) grammar (k…

A: explaination given as:

Q: 10. Show that the language is not regular. L = {a"! :n≥1}

A:

Q: Let us have the following regular grammarG. Apply the method of regular equations on conversion…

A: Regular expressions are a powerful tool for describing patterns in strings. They are used in many…

Q: 4. Consider the following languages. ANFAFIN = {{N) | N is an NFA and L(N) is finite} EREX = {(R) |…

A: Below is the answer to above question. I hope this will be helpful for you

Q: Proof that the language L1 = {a' b' c¹ | i≥ 1} is not Context Free.

A: The Answer is in step-2.

Q: Build a TM over the alphabet Σ = {a,b} that accepts the language where each word has twice as many…

A: TM stands for Turing Machine. Alan Turing invented the Turing machine in the year 1936.Turing…

Q: ANNSWER BY TRUE OF FULSE: (No need to explain as I already know the answer but I want to check my…

A: All possible patterns of strings can be represented with the help of CFG i.e., context free…

Q: 2. Do there exist regular languages L and L2 such that (L;UL2) = (Lol)? YES or NO

A: yes

Q: L= { anban bab | n ≥ 0 }

A: A context-free language (CFL) is a language generated by context-free grammar (Type 2 grammar) and…

Q: Q4: Let Σ = {0, 1, #} and define a language B over Σ as follows: B = {r#s: r,s = {0, 1}^*, r is a…

A: The task is to prove that the given language is not context free.Given :Σ = {0, 1, #} Language…

Q: What is the grammar G for the following language? L (G) = { 0 1 | n>=1 }

A: The language is : 0n 1n

Q: nguage L =

A:

Q: Construct a FA(in TG)that accepts the language generated by the RG. A →aB B →abA| b

A: Answer 1. We are given that the language ends with a or bbb and before that there can have any…

Q: Show that the language L = {a"b"+k : n > 0, k > 1} U {a"+*g" :n > 0, k > 3} is not regular.

A: Given language is, L={anbn+k : n>=0, k>=1} ∪ {an+kbn :n>=0, k>=3} Set of input…

Q: 3. Give a DPDA that accepts the language {(ab)*(ba)' : i > 0}

A: Answer:-

Q: L={w | w=a^n,b^m, n,m ≥0} is language .Design the deterministic finiteautomaton(DFA) that recognizes…

A: Given Language L= { w | w = an, bm, n,m ≥ 0} where Language L accepts either an or bm strings as…

Q: Let L, and L2 be the languages defined as follows: L1 ={ xe{0,1}* | x has an odd number of Os}. L2…

A: In this question, we have two languages L1 and L2 and asked the grammar for L1 U L2. L1 is a regular…

Q: The symmetric difference of two sets S, and S2 is defined as S1O S2 = {x:xE S, or xE S2, but x is…

A: Below is the answer to above question. I hope this will be helpful for you...

Q: Construct an nfa that accepts the language L((a|b)* ab(a|b))

A: A string is accepted by a NFA if at least one of all possible transitions ends in a final state.

Q: Context Free Grammar LetL={a^nb^n|n>0}. Show that L^k is context free for any given k greater than…

A: If there is a CFG for a language, then the language is said to be a Context Free Language

Q: Show the language L = {a"b*c": n 2 0, k 2 0} is not regular.

A: Pumping lemme is a powerful tool for proving certain language are non -regular.

Q: Consider two regular languages L1 and L2. Let L1 be infinite while L2 be finite. S: Every subset of…

A: Here in this question we have have given two regular language L1 and K2 .based on this we have asked…

Q: 2. What is the TG corresponding to the language of strings, over alphabet {a, b}, that are composed…

A: Given: What is the TG corresponding to the language of strings, over alphabet {a, b}, that are…

Q: Decidable Languages Let R and S are regular expressions. Show that the following language L is…

A: Given:

Q: Prove this Padding Lemma.

A: Padding lemma. Let e be an index of a partial recursive function φe .Then there is an infinite,…

Q: Construct npda’s that accept the following regular languages:   L1 = L(aaa*bab). L2 =…

A: SOLUTION -   (1)  L1 = L(aaa*bab).   Here, M = {Q, Σ, ?, Γ, q0 , Z0,F} Q={q0,q1,q2,q3,q4,q5} , Σ =…