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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
Q4:7- When a software keeps changing during its development A. Software Consistency B. Software Stability C. Software Durability D. Software Testability See Answer
Q5:8- 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
Q6:9- 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
Q7:10- 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
Q8:11- Which class is 100.1.3.0 belong to? A. Class A B. Class B C. Class C D. Class D See Answer
Q9:3. Describe the language defined by the following Grammar: (S) → (A)(B)(C) (A) → a(A) | a (B) → b(B)| b (C) →ESee Answer
Q10:5. 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
Q11:1. (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
Q12:2. (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
Q13:3. (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
Q14: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
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.See Answer
Q16: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
Q17: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
Q18:Problem 1 (23 pts.) Consider the following claim: Claim. {21n: n € Z} U {14n: n € Z} c{7n:n €Z}. (a) (3 pts.) Write the claim as an (equivalent) if-then statement. Grading Notes. While a detailed rubric cannot be provided in advance as it gives away solution details, the following is a general idea of how points are distributed for this problem. We give partial credit where we can. (3) Correctness. Regardless of how you formulate your proof, you will need to have an if-then statement that is equivalent to the original. (b) (11 pts.) Give a direct proof by cases that the claim is true. As a hint, you might want to prove the if-then statement you constructed in (a). To get full points you must use a mixture of formal notation and word explanations (e.g. the "column" format). Each step of your proof should have an explanation as to how/why you could make that logical step. When in doubt, more detail is better than less. Grading Notes. While a detailed rubric cannot be provided in advance as it gives away solution details, the following is a general idea of how points are distributed for this problem. If you can at least get part-way, we give partial credit where we can. (9) Correctness. If your proof is not correct, this is where you'll get docked. (2) Regardless of how you formulate your proof, you will need clearly labeled exhaustive cases. (6) Regardless of how you formulate your proof, somewhere you'll need certain facts without which the proof wouldn't work. E.g. if it weren't true that the sum of two integers is integer, would your proof fail? If so, then that is a fact I need to see stated somewhere. (1) The order of these facts makes sense, so that you're not inferring something before you have all the facts to infer it. E.g. you cannot use the fact that the sum of two integers is integer if you don't already know that you have two integers to begin with. The order of how you use these does not have to exactly match those in the sample solutions, but there are orders that will not work and you will lose points if, for example, you use "the difference of ints is int" before you use "the product of ints is int". If you combine some steps (such as "the difference and product of ints is int" or "the product of two non-zero ints is a non-zero int") that is fine. Just don't combine all (see below). (2) Communication. We need to see a mix of notation and intuition, preferably in the "column" format with the notation on the left, and the reasons on the right. If you skip too many steps at once, or we cannot follow your proof, or if your solution is overly wordy or confusing, this is where you'll get docked. (c) (3 pts.) State (but do not prove) the contrapositive of your statement from part (a). Grading Notes. While a detailed rubric cannot be provided in advance as it gives away solution details, the following is a general idea of how points are distributed for this problem. We give partial credit where we can. (3) Correctness. You have to have the contrapositive statement of whatever if-then state- ment you wrote in part (a). (d) (3 pts.) State (but do not prove) the converse of your statement from part (a). Grading Notes. While a detailed rubric cannot be provided in advance as it gives away solution details, the following is a general idea of how points are distributed for this problem. We give partial credit where we can. (3) Correctness. Regardless of how you formulate your proof, you will need to have an if-then statement that is the contrapositive of the original. (e) (3 pts.) Give a disproof by counter-example of the converse from part (d). (That is, show that the converse is not true by providing an example that demonstrates it is not true.) Remember that any disproof by counter-example not only provides the counter-example, but also an explanation as to why it is a counter-example. Grading Notes. Note that this problem gives you practice disproving a statement by counter-example, which requires clearly stating a counter-example, and then showing why it is a counter-example.See Answer
Q19:Problem 2 (13 pts.) Consider the following claim. Claim. For any sets S and T, (SxT)n (Tx S)-(Sx S) = 0. (a) (11 pts.) Use a proof by contradiction to prove the claim. To get full points you must use a mixture of formal notation and word explanations (e.g. the "column" format). Each step of your proof should have an explanation as to how/why you could make that logical step. When in doubt, more detail is better than less. Grading Notes. While a detailed rubric cannot be provided in advance as it gives away solution details, the following is a general idea of how points are distributed for this problem. We give partial credit where we can. (9) Correctness. If your proof is not correct, this is where you'll get docked. (5) Regardless of how you formulate your proof, somewhere you'll need certain facts without which the proof wouldn't work. E.g. if it weren't true that the sum of two integers is integer, would your proof fail? If so, then that is a fact I need to see stated somewhere. (1) The order of these facts must make sense, so that you're not inferring something before you have all the facts to infer it. E.g. you cannot use the fact that the sum of two integers is integer if you don't already know that you have two integers to begin with. (3) You also must use a proof by contradiction, which clearly states it is a proof by contradiction, states what the contradictory assumption is, finds a contradiction, and clearly states what and where that contradiction is. (2) Communication. We need to see a mix of notation and intuition, preferably in the "column" format with the notation on the left, and the reasons on the right. If you skip too many steps at once, or we cannot follow your proof, or if your solution is overly wordy or confusing, this is where you'll get docked. (b) (2 pts.) Is it possible to prove this claim by contrapositive? If so, what would the statement of the claim be (that you could then apply the contrapositive to)? If not, give a brief explanation why it cannot be done. Grading Notes. This problem is meant for you to think about whether you can modify your proof to be of a different form, and explaining your answer.See Answer
Q20:Consider the following semi-Thue system S1: a-aabc cb-bc prove thatSee Answer

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