HW 3: Given the regular expression ((a/b)(albb)): • Construct an equivalent NFA using Thompson's construction. • Convert this NFA to a DFA using the subset construction method.
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- HW 3: Given the regular expression ((alb)(a bb)): • Construct an equivalent NFA using Thompson's construction. • Convert this NFA to a DFA using the subset construction method.HW 2: Given the regular expression a*(a/b)aa: • Construct an equivalent NFA using Thompson's construction. • Convert this NFA to a DFA using the subset construction method.7. Use the set-roster notation to indicate the elements in eachof the following sets.a. V = {s ∈ Z| s > 2 or s < 3}b. W = {t ∈ Z | 1 < t < −3}c. X = {u ∈ Z | u ≤ 4 or u ≥ 1}
- Sets are collections (1) without defined order and (2) not allowing duplication. Multisets, also called “bags” are collections without defined order but which permit duplication, i.e., more than one element. We define the function #(a B) to be the number of occurrences of the element a in the bag B. For example, #(1, [1 1 2 3 4 4 5]) is 2 and #(5, [1 1 2 3 4 4 5]) = 1. Bag union and intersection are defined in terms of #. bag-union: List × List -> ListThis function should take as arguments two lists representing bags and should return the list representing their bag-union. bag-intersection : List × List -> ListThis function should take as arguments two lists representing bags and should return the list representing their bag-intersection. Allowed functions. Your code must use only the following functions:1. define, let2. lambda3. cons, car, cdr, list, list?, append, empty?, length, equal?4. and, or, not5. if, cond6. +, -, /, * Racket code only please. Thank you!Sets are collections (1) without defined order and (2) not allowing duplication. Multisets, also called “bags” are collections without defined order but which permit duplication, i.e., more than one element. We define the function #(a B) to be the number of occurrences of the element a in the bag B. For example, #(1, [1 1 2 3 4 4 5]) is 2 and #(5, [1 1 2 3 4 4 5]) = 1. sum : List × List -> List This function should take as arguments two lists representing bags and should return the list representing the list resulting from simply appending the input lists together. Racket code only please. No loops Allowed: 1. define, let2. lambda, curry3. cons, car, cdr, list, list?, append, empty?, length, equal?4. and, or, not5. if, cond6. map, append-map, andmap, ormap, filter, apply7. +, -, /, * Thank you!Sets are collections (1) without defined order and (2) not allowing duplication. Multisets, also called “bags” are collections without defined order but which permit duplication, i.e., more than one element. We define the function #(a B) to be the number of occurrences of the element a in the bag B. For example, #(1, [1 1 2 3 4 4 5]) is 2 and #(5, [1 1 2 3 4 4 5]) = 1. Bag union and intersection are defined in terms of #. bag-union: List × List -> List This function should take as arguments two lists representing bags and should return the list representing their bag-union. bag-intersection : List × List -> List This function should take as arguments two lists representing bags and should return the list representing their bag-intersection. Allowed functions. Your code must use only the following functions:1. define, let2. lambda, curry3. cons, car, cdr, list, list?, append, empty?, length, equal?4. and, or, not5. if, cond6. map, append-map, andmap, ormap, filter, apply7. +, -,…
- Sets are collections (1) without defined order and (2) not allowing duplication. Multisets, also called “bags” are collections without defined order but which permit duplication, i.e., more than one element. We define the function #(a B) to be the number of occurrences of the element a in the bag B. For example, #(1, [1 1 2 3 4 4 5]) is 2 and #(5, [1 1 2 3 4 4 5]) = 1. Bag union and intersection are defined in terms of #. bag-union: List × List -> ListThis function should take as arguments two lists representing bags and should return the list representing their bag-union. bag-intersection : List × List -> ListThis function should take as arguments two lists representing bags and should return the list representing their bag-intersection. Allowed functions. Your code must use only the following functions:1. define, let2. lambda3. cons, car, cdr, list, list?, append, empty?, length, equal?4. and, or, not5. if, cond6. +, -, /, * No loops or use of hash Racket code only please.…Sets are collections (1) without defined order and (2) not allowing duplication. Multisets, also called “bags” are collections without defined order but which permit duplication, i.e., more than one element. We define the function #(a B) to be the number of occurrences of the element a in the bag B. For example, #(1, [1 1 2 3 4 4 5]) is 2 and #(5, [1 1 2 3 4 4 5]) = 1. sum : List × List -> ListThis function should take as arguments two lists representing bags and should return the list representing the list resulting from simply appending the input lists together. Racket code only please. No loops Allowed: 1. define, let2. lambda3. cons, car, cdr, list, list?, append, empty?, length, equal?4. and, or, not5. if, cond7. +, -, /, * Thank you!Introduction For this assignment, you are to write a program which implements a Sorted List data structure using a circular array-based implementation and a driver program that will test this implementation. The Sorted List ADT is a linear collection of data in which all elements are stored in sorted order. Your implementation has to store a single int value as each element of the list and support the following operations: 1. add(x) – adds the integer x to the list. The resulting list should remain sorted in increasing order. The time complexity of this operation should be 0(N), where N is the size of the list. 2. removefirst() - deletes the first integer from the list and returns its value. The remaining list should remain sorted. Time complexity of this operation should be 0(1). 3. removelast() – deletes the last integer from the list and returns its value. The remaining list should remain sorted. Time complexity of this operation should be 0(1). 4. exists(x) – returns true if the…
- Describe each of the following sets.a. {x ∈ R|−5 < x < 1}b. {x ∈ Z|−5 < x < 1}c. {x ∈ Z−|−5 < x < 1}Regular expression to NFA to DFA conversion: Describes the process of taking a unique regular expression, converting that regular expression to an NFA, then converting the NFA into a DFA. Your regular expression must have at minimum two union, two concatenation, and two Kleene star operations. As followed, concatenations of single charaters can be condensed. Your regular expression cannot be a solved problem from any book. You should describe the regular expression with both processes to convert the regular expression to an NFA and the conversion of that NFA into a DFA.Describe each of the following sets by listing its elements:a. {x | x ∈ N and x2 − 5x + 6 = 0}b. {x | x ∈ R and x2 = 19}c. {x | x ∈ N and x2 − 2x − 8 = 0}}d. {x | x ∈ Z and x ∗ x = 4}