2.26 Show that if G is a CFG in Chomsky normal form, then for any string w E L(G) of length n > 1, exactly 2n – 1 steps are required for any derivation of w.

Q: Show that (-p q) is equivalent to (p -q). Show that (q A (- (-q Vp))) v (p^ q) is equivalent to q.…

A: Here, we are going to show that given propositions are equivalent using prepositional equivalences.…

Q: x)∗f(y) • f(x′) = (f(x))′′ (a) Prove f(0) = 0∗ (b) Give an example of a homomorphism from P({1,2,3})…

A: A function from Boolean algebra B to Boolean algebra B∗ is a homomorphism if it satisfies the…

Q: Show that (¬ p ∨ q) ↔ ((p ∧ ¬q) is a tautology

A: Given equation is, (¬ p ∨ q) ↔ ((p ∧ ¬q) It contains two variables pa and q. Tautology means, for…

Q: Let L be any regular language over {a, b, c}. Show how the Pumping Lemma can be used to demonstrate…

A: The Answer is in step2

Q: 5. Show that (p A q) → r and (p → r) ^ (q → r) is logically equivalent.

A: Defined the given expression is logically equivalent

Q: Let E = {a, b} and L = {ww|w e E and w is of length k}. Show that for each k, no DFA can recognize…

A: We need to show that DFA can't be less than 2^k states for given scenario.

Q: 8. Show that ¬p → (p → q) is a tautology using rules.

A: p q ~p p -> q ~p -> (p ->q) T T F T T T F F F T F T T T T F F T T T

Q: 1. Show that the language of even strings over (0,1) that begin and end with 0 is regular. Give both…

A: The Answer is

Q: Consider the following resolution proof: 1. р(x) P 2. q(y, a) V ¬p(a) 3. q(а, а) P 4. ду, а) 5. да,…

A: Lets see the solution in the next steps

Q: not L is empty, we need only test at most (3n − 1)/2 strings.

A: Determined the given language L is not  empty

Q: Let E={〈M〉| M is a TM and every string in L(M) has even length}. Argue that the property described…

A: I Have answered this question in step 2.

Q: 2) Is aa distinguishable from bb with respect to the set of strings over {a,b} that have an even…

A: ^b*(ab*ab*)*$^a*ba*(ba*ba*)*$The first regular expression ensures  there are an even number of a…

Q: 3 Even Let INFINITETM = { | M is a TM that accepts an infinite number of strings} Prove whether…

A: Hi there, Please find your solution below, I hope you would find my solution useful and helpful.…

Q: Show that [¬P∧ (P ∨ Q) ]→Q is tautology using laws of equivalences

A: Given logic is,  [¬P∧ (P ∨ Q) ]→Q Variables present in this function are P, Q.

Q: Let R = (J,K, L, M, N, P) and F = {J → KL, L → J, MNP → K, KP – M, LJ → N}, give a canonical cover…

A: As per guideline, I can do only first one. Please re-post pending question in next post. I hope you…

Q: 9. A computer system considers a string of the digits 0, 1, 2, 3 a valid codeword if it has no two…

A: Answer is given below with full description

Q: ● Example 3.4: let F = A'C + A'B + AB'C + BC a) Express it in sum of minterms. b) Find the minimal…

A:

Q: Let L be an arbitrary language over {0,1}*. Show that L is r.e. if and only if L reduces to ATM.

A: Regular expression for arbitrary language {0,1}*: The set of all strings in {0,1}* with an odd…

Q: Given two strings r = x1x2··· In and y = common subsequence, that is, the largest k for which there…

A: Given two questions are not interlinked. As per our guidelines, only one will be answered. So,…

Q: A natural number is composite if and only if it is not prime. Give a non-deterministic TM over the…

A: Answer: I have given answer in the handwritten format.

Q: Use the pumping lemma to prove that the language L over {a,b,c}", given by L = {wcv: |wa = |vl6} is…

A: First lets see Pumping lemma for regular languages: If a language L is regular, then there exist an…

Q: Let L be any regular language over {a, b, c}. Show how the Pumping Lemma can be used to demonstrate…

A: Pumping Lemma is used as a proof for irregularity of a language. Thus, if a language is regular, it…

Q: For the following directed graph, let E = {I,J,K,L,M} and let V = {a,b, c, d}. %3D a d M b K For…

A: Given graph contains, 5 edges= {I, J, K, L, M} 4 vertices= {a, b, c, d} Indegree of the vertex is,…

Q: Let L be the language L-(anbmc2n | (n+2n)>m) over the alphabet E-(a,b,c). Prove that L is not…

A:

Q: Consider a DFA over E = {a, b} accepting all %3D strings which have number of a's divisible by 6 and…

A: Introduction :We have asked for the numbers of states in the DFA which will accept the string which…

Q: Let Fn represent the Fibonacci sequence Fo =0, Fi=F,, and V nzz defined by Fr- F,tEz n-2 z 2U A…

A: The proof is below:

Q: Prove the implication rule.That is, prove that (P → Q) ↔ (P′ ∨ Q) is a tautology.

A: Any expression with some logical notations can be stated as "Tautology" if all the expression…

Q: & be a graph. (a) State a bound on x(G) in terms of the maxi- mum degree of G. (b) If x(G) = 2, show…

A: The chromatic number of a graph GG is the minimum number of colors required in a proper coloring; it…

Q: Show that ( X→ Y ) ∨ ( Y →X) is a tautology.

A: To solve this,  segregate each expression into different parts- ( X→ Y ) - If X is true and Y is…

Q: d = F4(W, X, Y, Z) = Em(0, 2, 3, 5, 6, 8) K-map for d: wx\YZ 00 01 11 10 00 01 0. 1 11 X. 10 1 101

A: Note: we had provided solution according to given K-map Table

Q: Let M be a FSM with n states. Let p and q be distinguishable states of M and let x be a shortest…

A: A finite deterministic automation M (transducer, Mealy machine, n M (transducer, Mealy machine,…

Q: Prove that {V, ^, +} is not an adequate set of connectives.

A: It is proven that the set {∨,∧,<->} is adequate.

Q: Draw a Karnaugh map for the following function; X= [m(0, 2, 3, 6, 7, 8, 10, 11, 14, 15) Then…

A:

Q: Prove that L= {uw e {a,b, c, d}* | #of) = #6(w) = #c(w) = #a(w)} is not context-free. (Hint: No need…

A:

Q: Let A %3D (с, n, b), В%3 (х, у) and C %3 (0, 1). Find a) AXBXC b) СХВХА с) ВХСХ

A: The cartesian product of 3 sets produces another set such that, the new set has tuples of 3 elements…

Q: Let L be the language L-{anbmc2n | (n+2n)>m) over the alphabet Σ=(a,b,c). Prove that L is not…

A:

Q: Pick and answer one of the two questions below: a. Prove that the language L = {w1*lw e {0, 1}+ and…

A: It is defined as a context-free language, there is a pumping length p such that any string w ∈ L of…

Q: 2- Let be f(t) a real, periodic function satisfy f(-t)= -f(t), The general form of the Fourier…

A: A Fourier series is an extension of a periodic function f(x) in terms of an infinite sum of sines…

Q: Problem 4 Prove L = {w {b,c}* | w has equal number of b's and c's, and for all prefix u of w, the…

A: L={W={b,c}*|} prove that is regular or not

Q: 9. Show that (p V q) ^ (¬p V r) → (q V r) is a tautology.

A:

Q: 1. Let M be the PDA below: a λ/A a A/λ bλ/B b B/λ 22/2 a) Give the transition table of M. b) Trace…

A: According to the information given:- We have to follow the PDA and create transition table of M,…

Q: Qn) Frame regular sets for the following and also give the corresponding regular expression. For E =…

A: Before solving above question we need to understand what is kleen's  theorem:- So basically…

Q: 2.Use the method of proof by contradiction to show that [(pvg)^(p→r)^(q→r)]→r r is a tautology.

A: Use the method of proof by contradiction to show that  [(p∨q)∧(p→r)∧(q→r)]→r is  a tautology

Q: 5. Let f:X→Y and g:Y→Z be one-to-one correspondences. (a) Prove that g◦fmust be a one-to-one…

A:

Q: Let U={a,b,c,d,e,f,g), A={a,b,c,d,e}, B={a,b,c,f) C={a,e,f,d,g): find :l Jgull *? complement of…

A: As per our guidelines we are supposed to answer only one question. Kindly repost the remaining…

Q: 1. Prove that p E F- [p] E F$. (Hint: the forward direction is immediate. For the converse, consider…

A: Solution: \documentclass{article} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{enumerate}…

Q: Given two strings A[1..n] and B[1..m], such that n >= m, propose an al- gorithm to find the number…

A: Answer is given below-

Q: Show that the language of strings over {1} of the form 1^n where n is a Fibonacci number is not…

A: -> To prove L is not regular , Pumping Lemma should be used.  -> Proof that above question is…

Q: Using Kleene's theorem, build a FA that defines the language L over the alphabet Σ = {0,1}, as given…

A: Please give positive ratings for my efforts. Thanks.   ANSWER   Here, J =  language of strings that…