For any string w over ∑, writing its individual symbols so that w = w1w2…wn, we define the reverse wR of w as simply w written backwards: Given w = w1w2…wn with wi ∈ ∑ for 1 ≤ i ≤ n, wR = wn…w2w1. Similarly, for any language A over ∑, we define its reverse language as the language containing the reverse of all its strings: Given a language A, AR = { wR | w ∈ A}. Show that the class of  context-free languages is closed under reversal

Q: Give a regular expression for the language of all strings over alphabet {0,1} that have exactly…

A: Given: A regular expression for the language of all strings over alphabet {0,1} that have exactly…

Q: For any string w over ∑, writing its individual symbols so that w = w1w2…wn, we define the reverse…

A: Given: w = w1w2…wn with wi ∈ ∑ for 1 ≤ i ≤ n, Reverse of w is denoted by wR . wR = wn…w2w1 Let A be…

Q: Consider the language of all strings which contain two consecutive 0 that ? = {11, 111, 110, 011,…

A: We need to find a RE for all strings which contain two consecutive 0.

Q: Let L be a language over the alphabet Σ = {a,b,c}. Prove that L = {abman for any positive integers n…

A: Regular language is a language which can be expressed using a regular expression or using finite…

Q: LetΣ ={a, b}. LetL={aibai|i≥0}.Give a Turing machine (TM) that accepts the languageL.Assume (as in…

A:

Q: Prove that A = {www|w is a string from {a,b}*} is not regular. Consider the string s=apbapbapb

A: Prove that the given expression is not regular Assume that A is regular. Let p1 be the pumping…

Q: Consider the language L = {a'b'c* | i # j,j # k, i # k}; it is not a context- free language. Show…

A: Pumping lemma for CFL is used to prove the language is not cfl using some valid string s.  Never use…

Q: Consider the following languages over the alphabet Σ = {a,b, c} L₁ = {a¹ b¹ck: i, j, k € N such that…

A: The pumping lemma for regular languages can be defined in such a way that it is a crucial end result…

Q: A palindrome is a string that reads the same backward as forward, i.e., w = wR. A palindromic…

A: Hey there, I am writing the required solution of the questin mentioned above. Please do find the…

Q: (a) L = {all words with exactly one b}. (b) L = {all words with at least one a}. (c) L = {all words…

A: For the alphabet Σ ={a, b}, construct an FA that accepts the following languages.(a) L = {all words…

Q: For any string w = wi w2 .. Wn, the reverse of w, written w", is the string w in reverse order, w,…

A: A is regular There is a DFA with I, initial state, {F1, F2, ..} Final states Let's Modify the DFA…

Q: 2. Let RE be the set of regular expressions over alphabet E = {0, 1}, and for r E RE, let L(r) be…

A: Regular Expressions Just as finite automata are used to recognize patterns of strings, regular…

Q: A language L is called slithy if it contains at least two strings and has the following property:…

A: The answer to the question is given below:

Q: Suppose L = {wlw does not contain the substring 11 is a language over the alphabet {0, 1}. Prove…

A: To formally prove that the language L = {w | w in {0,1}* and w does not contain the substring "11"}…

Q: dæ Vy (E(x,y) → B(x) ^ W (y))

A: Given,  B(x)  x is a bird W(x)  x is a worm E(x, y)  x eats y The different symbols are…

Q: Draw a deterministic finite automaton (DFA) that recognizes the language consisting of strings over…

A: Solution: DFA that except exactly two a's (which not be consecutive) and any number of b's or…

Q: Given N = (Q, {a, b}, δ, q0, F) is an NFA that recognizes language L. Define a new language…

A: To construct an NFA that recognizes a language L, we will need to define a set of states, an…

Q: Consider the language L = { 3x such that x = L(M₁) L(M₂)}. Show that L is not decidable.

A: To prove that the language L is not decidable, we need to show that there is no Turing machine that…

Q: Assume that we want to use the Pumping Lemma to prove the language L is not a regular language. Here…

A: The objective of the question is to use the Pumping Lemma to prove that a given language L is not a…

Q: Exercise 6 (Ex. 17, Chapter 2 of (Martin; 2011). Let L be the language AnBn = (a"b" In2 0). a. Find…

A: Let  L ⊆ Σ * be any language and Two strings 'x' and 'y' belong to it now language L is called…