E→E+T T T→TXF|F F→ (E) | a
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2.11) Convert the CFG G4 given in Exercise 2.1 to an equivalent PDA, using the procedure given in Theorem 2.20.
I Attached Exercise 2.1 below
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- My apologies for misunderstanding. Here's the translation: "A function, f:f(x,y)=x2+2y2−12x+xy is defined on the domain: Ω = {(x, y): -1 ≤ x ≤ 1, -1 ≤ y ≤ x}. Create a contour plot of the function and plot the boundary of Ω with a dashed line: In PythonI'm having a difficult time with this problem. Could you lend me a hand in understanding it? I'd appreciate a step-by-step explanation, along with insights into how you arrived at the solution. here is the question I need help with:4.3 Let ALLDFA = {<A> | A is a DFA and L(A) = Σ∗ }. Show that ALLDFA is decidableGiven the function g(x1,..., x4) = m(0, 2, 4, 5, 10, 11, 13, 15), answer the following questions: a) How many possible implicants for g? b) Find all prime implicants. c) Find all essential prime implicants. d) Derive the equivalent logical expression with the minimum number of Literals.
- c. Briefly discuss the count to infinity problem in the DV algorithm by changing the link cost D(X,Y) for the worse from 4 to 60 and showing the painfully slow convergence from the converged distance vector configuration in 1. a. (You may stop after a few iterations and indicate the number of iterations required for full convergence.Question For each of the following, determine whether argument is valid. You may use a counterexample or equivalence transformations to justify your answer. (a) P→ q (b) (c) קר :: 79 P→r q→r ¬(pv q) :: r P→r q→r qV¬r :: 19(b) Let C(x, y) mean that "student x has taken course y", where the domain for x consists of all students at your school and the domain for y consists of all courses offered at the university. Express each of these sentences in terms of C(x, y), quantifiers, and logical connectives. (i) Not every student has taken the course SWEN2002. (ii) Laila has taken every course except for SWEN3000. (iii)Kayley has taken exactly one course. (c) Write each of the following statements in the form if p, then q. (i) Shane has an allergy whenever he eats peanuts. (ii) It is necessary to have studied abroad to have the full experience of university. (iii)Rich will yell unless the children do not walk on his lawn. (d) Given the hypotheses, mk and (-h A-k)→ -p, m A p show that-h→m is a valid conclusion.
- 3.15 Simplify the following Boolean function F, together with the don't-care conditions d, and then express the simplified function in product of sums form: (c) F(A, B, C, D) = Σ(5, 6, 7, 12, 14, 15,) (d) d(A, B, C, D) = Σ(3, 9, 11, 15) F(A, B, C, D) = Σ(4, 12, 7, 2, 10,) d(A, B, C, D) = Σ(0,6,8)Question 7 • Given pda for {d'b'c* | i = j + k} (a, ɛ/X) (b, X/ɛ) (c, X/ɛ) (E, ɛ/ɛ) Draw a PDA for {d'b'ď | i>j+k} Draw a PDA for {a'b'c* | iConsider the following segment of code. Assume that i, z, and n are integers, and that n ≥ 0. . State a non-trivial loop invariant (must include two conditions: one each for i and 2). • Prove the invariant. A correct proof using an incorrect invariant would still receive credit. . Be sure the proof includes the final conditions after the loop has ended. Show the final value of z in terms of n. // (n ≥ 0) i = 0; x = 3; 11 while i1. Prove formally that the following statements are equivalent: For any two formulas A and B, (a) A = B; (b) A → B is valid; (c) A^¬B is unsatisfiable.Question b only QUESTION 1 Let G be the CFG over E = {a, b} given by the rules: %3D S - X|Y | Z + €| aaY Y + E| Zbb Z + e|aXb it. Make sure you consider the empty string e. Give a derivation for each accepted word. (b) Using the construction we saw in the lecture, construct a PDA A such that L(G) = L(A). %3D (e) Test your constructed PDA on each of the words you considered in (a) by giving an You only have to answer question bReduce the following lambda-calculus terms to the normal form. Show all intermediate steps, with one beta reduction at a time. In the reduction, if necessary, assume that you are supplied with extra rules that allow you to reduce the addition of two natural numbers into the corresponding result. (λz. z) (λy. y y) (λx. x a)Recommended textbooks for youDatabase System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill EducationStarting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSONDigital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSONC How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSONDatabase Systems: Design, Implementation, & Manag…Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage LearningProgrammable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill EducationDatabase System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill EducationStarting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSONDigital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSONC How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSONDatabase Systems: Design, Implementation, & Manag…Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage LearningProgrammable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education