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Q1:1- Mealy and Moore FSM depend on? a. Mealy FSM depends on present state and present input b. Moore FSM depends on present state only See Answer
Q2:4- When the developers make the program in an architecture such that it can be used by other customers in the future A. Customer-specific program B. Program files C. Program generator See Answer
Q3:6- what is changing one requirement, while taking into account competing requirements A. Software Feasibility B. Software Consistency C. Software Maintainability D. Software Stability See Answer
Q4:8- In database ER diagram, how do we uniquely identify relationships? A. Primary key of participating entities B. Primary key of the relation itself C. By its attributes D. Relationships cannot be uniquely identified See Answer
Q5:9- What is a foreign key? A. Primary key of a participating relation B. Super key C. Composite key D. Primary key of a relation See Answer
Q6:10- Given a K-map with one 1 circled and the equation is ABCD (ANDed), what is it? (third circle in the first row) A. Minterm B. Maxterm C. Prime implicant D. Essential prime implicant See Answer
Q7:11- Which class is 100.1.3.0 belong to? A. Class A B. Class B C. Class C D. Class D See Answer
Q8:3. Describe the language defined by the following Grammar: (S) → (A)(B)(C) (A) → a(A) | a (B) → b(B)| b (C) →ESee Answer
Q9:5. Convert the below BNF into EBNF. (program) → begin (stmt_list) end (stmt_list)→→ (stmt) |(stmt); (stmt_list) (stmt) → (var) = (expression) (var) → A|B|C (expression) → (var) + (var) | (var) - (var) | (var)See Answer
Q10:1. (40 pt., 10 pt. each) Construct a Turing machine in JFLAP (version 7.1) that decides each of the following languages. For each language, you must submit one JFLAP file clearly labeled (e.g., 1a.jff). Make sure that you test your Turing machines in JFLAP before submitting. Note: there is no explicit reject state for Turing machines in JFLAP. You should assume that there is a transition to the reject state whenever a state is missing a transition for a particular symbol. a. A = {we {a,b}* | w contains at least one a and at most one b} b. B = {w € {a,b}" | w contains more a's than b's} c. C = {a¹b/c+/|ij≥0} d. D= {0¹1 |n, m≥ 0 and n is divisible by m} For example, 000011 € D (because 4 is divisible by 2) and 00011 # D (because 3 is not divisible by 2).See Answer
Q11:2. (40 pt., 10 pt. each) Give an implementation-level description of a Turing machine that decides each of the languages in Problem 1. a. A = {w = {a,b}* | w contains at least one a and at most one b} b. B = {w = {a,b}" | w contains more a's than b's} c. C = {a¹b/citii,j ≥ 0} d. D= {01m|n, m≥ 0 and n is divisible by m} For example, 000011 € D (because 4 is divisible by 2) and 00011 # D (because 3 is not divisible by 2).See Answer
Q12:3. (20 pt.) Prove that the following language is not context-free using the pumping lemma. E = {a¹b/ck | i≤j, i ≤ k, and i, j, k ≥ 0}See Answer
Q13:Problem 1 There are two parts: [Lecture Slides 10, page 18]: (a) Prove one side of the equivalence in the exercise in [Lecture Slides 13, page 32], specifically Þ→ V (not → Þ), after replacing and, by propositional variables p and qi, for i = 1, 2, 3. (b) Prove one side of the equivalence in the exercise in [Lecture Slides 13, page 33], specifically Þ→ V (not V $), after replacing ; and ; by propositional variables p; and q₁, for i = 1, 2, 3, but leave as a generic (i.e., unknown) wff with two free variables. In both parts, we ask you to choose a proof-theoretic, not semantic, approach. Proof-theoretically, you can choose natural deduction or also tableaux, even though in the case of tableaux we have not yet mentioned expansion rules for quantifiers in lecture (but these are easy to formulate - left to you!).See Answer
Q14:Problem 3 There are two parts: (a) [EML.Chapter_2.pdf, page 32]: Do part 1 of Exercise 48. (b) [EML. Chapter_2.pdf, page 33]: Do part 3 of Exercise 48.See Answer
Q15:Problem 3 There are two parts: (a) [EML.Chapter_2.pdf, page 32]: Do part 1 of Exercise 48. (b) [EML.Chapter_2.pdf, page 33]: Do part 3 of Exercise 48. In your solutions for Problem 4, Problem 5, and Problem 6 as LEAN_4 scripts, you may want to include the following imports from the LEAN_4 library (possibly not all of them, but you will have to experiment to find out if all are needed): import Mathlib.Data.Real. Basic import Mathlib. Tactic. Interval Cases import Library. Theory. Comparison import Library. Theory. Parity import Library. Theory. Prime import Library. Tactic. ModCases import Library. Tactic. Extra import Library. Tactic. Numbers import Library. Tactic. Addarith import Library. Tactic. Cancel import Library. Tactic. UseSee Answer
Q16:Write a program that accepts as input a description of a nondeterministic finite automaton with E-moves (NFA-e) over the alphabet Σ = {a,b} followed by a sequence of one or more words. Your program should simulate the NFA-e and report whether each word was accepted or rejected by the NFA-€.See Answer
Q17:1. Deterministic Construction [9 points] Consider the language A over the alphabet Σ = {0,1}: A = {w: w has 1 as one of the last three digits} (a) Generate the state diagram for a DFA which decides A. (b) Give the 5-tuple which represents your DFA from 1(a). You may use a table to represent the transition function 8.See Answer
Q18:2. Nondeterministic Construction [6 points] Generate the state diagram for an NFA which decides the language B over the alphabet Σ = {a,b}: B = {w: w contains 'aa' or 'ab'}See Answer
Q19:3. NFA to DFA Conversion [8 points] Convert the following NFA to an equivalent DFA which decides the same language: 0,1,2,3 0,1,2,3 B 3 ESee Answer
Q20:4. Closure in Reverse [7 points] Suppose that L is an arbitrary regular language. Prove that LR, the reverse of L, is also regular. If a string w is in L, the reverse of that string, w, is in LR. The reverse operation is defined recursively as: • ER = E For a string w and symbol a € E, (wa) = a(w) i.e. (110) R = 011.See Answer

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