S is a set of strings recursively defined as follows. Base case: Every variable from the set {a, b, c, d, e, ƒ} is in S. Recursive rules: If x € S and y = S, then: 1. (x + y) € S 2. x-yЄ S Indicate which expressions are in S. (d.e.a) a+b a.b.c ☐ (a+d).e
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- S is a set of strings over the alphabet {a, b}* recursively defined as: Base case: λ ∈ S, a ∈ S, b ∈ S Recursive rules: If x ∈ S, then Rule 1: axb ∈ S Rule 2: bxa ∈ S List all the strings in S of length 3.language: Python Problem: Write a recursive function reverse(sentence) for reversing a sentence. For example, reverse('Who let the dogs out?') will return '?tuo sgod eht tel ohW'. Also write a test case in the program to prove the function given works.A palindrome is a string that reads the same forwards or backwards; for example dad, mom, deed are palindromes (i.e., reversing a palindrome produces the same string). Use C++ Programing language Write a recursive, boolean-valued function, isPalindrome that takes a string as a parameter and returns whether the string is a palindrome. A string, s, is a palindrome if: s is the empty string or s consists of a single letter (which reads the same back or forward), or the first and last characters of s are the same, and the rest of the string (i.e., the second through next-to-last characters) form a palindrome. Write a test program that reads a string from the standard input device and outputs whether the input string is a palindrome or not.
- Prolog The sequence of Pell numbers 0,1,2,5,12,29,70,169,408,.. can be defined recursively as the sequence of numbers in which the first two numbers are 0 and 1, and each subsequent number is given by adding 2 times the preceding number to the number which precedes this. This can be defined in Haskell as: pell :: Int -> Int pell 0 = 0 pell 1 = 1 pell n = 2 * pell (n-1) + pell (n-2) Formulate the appropriate Prolog predicate "pell(N,Pn)" which is true if (and only if) "Pn" is the "N"-th term of the sequence of Pell numbers (note that we start numbering the sequence of Pell numbers with 0). That is, "pell(8,408)." would evaluate to "true", or "pell(5,Pn)." would give "Pn = 29"Regular expressions are built recursively out of smaller regular expressions, using some rules described below. Each regular expression ?denotes a language ?(?), which is also defined recursively from the languages denoted by ?′? subexpressions. Given an alphabet ∑ = {0, 1}, write the language denoted by the following regular expressions:(i) 1(ii) 0 | 1(iii) (0 | 1)(iv) (0 | 1)∗(v) 1(0 | 1)∗(vi) 0 |1 (0| 1)Each regular expression r denotes a language L(r), which is also defined recursively from the languages denoted by r ′s subexpressions. Write the language denoted by the following regular expressions:(i) a |a*b (ii) a(a | b)* (iii) (a | b)*ab (iv) a | b
- write a dynamic programming algo (bottom-up or recursive) with input strings A and B, that solves Edit Distance in time O(|A| · |B|).Use the recursive descent parser in Section 4.4.1 below for the string a + b + c <expr> → <term> {(+ | -) <term>} <term> → <factor> {(* | /) <factor>} <factor> → id | int_constant | ( <expr> )def height(words, word): The length of a word is easy enough to define by tallying up its characters. Taking the road less traveled, we define the height of the given word with a recursive rule for the height of the given word to follow from the heights of two words whose concatenation it is. First, any character string that is not one of the actual words automatically has zero height. Second, an actual word that cannot be broken into a concatenation of two nonempty actual words has the height of one. Otherwise, the height of an actual word equals one plus the larger of the heights of the two actual words whose combined concatenation it can be expressed as. To make these heights unambiguous for words that can be split into two non-empty subwords in multiple ways, this splitting is done the best way that produces the tallest final height. Since the list of words is known to be sorted, you can use binary search (available as the function bisect_left in the bisect module) to quickly…
- Alert dont submit AI generated answer. Consider the following implementation of function multiply.int multiply ( int x , int n ) {if ( n <= 0 ) {return 0 ;}else {return x+m u l t i p l y ( x , n −1 ) ;}}a) Briefly explain why this implementation is not tail-recursive.b) Give a tail-recursive implementation in the C language. You might need todefine a helper function.c) Give an equivalent loop-based implementation of the same function in the Clanguage. You are only allowed to use a while loop for this question.Determine whether a string is a palindrome A palindrome is a string of characters that reads the same from right to left as it does from left to right, regardless of punctuation and spaces. Some famous English palindromes include the following “Madam, I’m Adam”, and “Never odd or even”. Of course, a simpler example would be the world “radar”.The specifications for this assignment are: Write and test a non-recursive solution in Java that determines whether a string is a palindrome •Your program should consist of at least two methods: (1) the main method (2) the method which performs the task of determining whether the specified string is a palindrome. You should name this method isPalindrome. You should name the class that contains your “main” method and the isPalindrome method FindPalindrome. •You must use a Stack and a Queue in your solution:Make sure to Write your own Stack and Queue based on the Vector in the Java API and use those in your solution. You should name those classes…Write a recursive function that takes a positive integer and returns the factorial of that integer. Attention, the function must be recursive, and its name must be "fatorial".