![PROBLEM #6. consider the alphabet: 22 = {[0 0], [0 1), (10), (1 1]]. Here, , contains all rows of Os and 1s of size on row).](http://img.homeworklib.com/questions/de90d2c0-0213-11ec-b2fb-516be7ac90a1.png?x-oss-process=image/resize,w_560)
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![w Strings in : @ flow (109 (003) -> To (6 { [0, 1] 0, D Co] o o a 4 twice twice (1) Stings not in Li- (9) { [01] (11] } =) 17](http://img.homeworklib.com/questions/fe2d1a60-0213-11ec-84e9-13faf58c0ded.png?x-oss-process=image/resize,w_560)
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PROBLEM #6. consider the alphabet: 22 = {[0 0], [0 1), (10), (1 1]]. Here, ,...
Suppose the alphabet is sigma = {a, b, ..., z, 0, 1, ..., 9,: }, i.e.,...
Suppose the alphabet is sigma = {a, b, ..., z, 0, 1, ..., 9,: }, i.e., the standard letters a-z, decimal numbers, and colon (: ). The colon is used as a delimiter between fields in a text file. Each line of the file thus corresponds to a string. a) Give a regular expression that accepts strings with four fields (i.e., with 3 delimiters). b) Give a regular expression that accepts strings where the second field is numerical. c) Give...
6. (10 pts) Is L regular? Either prove that it is not regular using pumping lemma,...
6. (10 pts) Is L regular? Either prove that it is not regular using pumping lemma, or describe an RE for it. The alphabet of the language is 10,1, +,-) L = { x = y + z | x, y, z are binary integers, and x is the sum of y and z }. For example, strings 1000 = 101 + 11, 0101 = 010 + 11, and 101 = 101 + 0 are in the language, but strings...
1. Consider the alphabet {a,b,c}. Construct a finite automaton that accepts the language described by the...
1. Consider the alphabet {a,b,c}. Construct a finite automaton that accepts the language described by the following regular expression. 6* (ab U bc)(aa)* ccb* Which of the following strings are in the language: bccc, babbcaacc, cbcaaaaccbb, and bbbbaaaaccccbbb (Give reasons for why the string are or are not in the language). 2. Let G be a context free grammar in Chomsky normal form. Let w be a string produced by that grammar with W = n 1. Prove that the...
Let Σ = {0, 1). (a) Give a recursive definition of Σ., the set of strings from the alphabet Σ. (b) Prove that for every n E N there are 2" strings of length n in '. (c) Give a recursive d...
Let Σ = {0, 1). (a) Give a recursive definition of Σ., the set of strings from the alphabet Σ. (b) Prove that for every n E N there are 2" strings of length n in '. (c) Give a recursive definition of I(s), the length of a string s E Σ For a bitstring s, let O(s) and I(s) be number of zeroes and ones, respectively, that occur in s. So for example if s = 01001, then 0(s)...
In Python import numpy as np Given the array a = np.array([[1, 2, 3], [10, 20,...
In Python import numpy as np Given the array a = np.array([[1, 2, 3], [10, 20, 30], [100, 200, 300]]), compute and print the sums over all rows (should give [6, 60, 600]) the sums over all columns (the sum of he first column is 111) the maximum of the array the maxima over all rows the mean of the sub-array formed by omitting the first row and column the products over the first two columns (hint: look for an...
Consider the language defined over the alphabet Σ (0, 1): [10] 2nin i. Show that L1...
Consider the language defined over the alphabet Σ (0, 1): [10] 2nin i. Show that L1 is context-free by specifying a CFG Gi for L1 ii. Convert the CFG Gi to a pushdown automaton Pv that accepts L1 by empty 12 stack iii. Give a pushdown automaton PF that accepts L by final state
Let M be an n x n matrix with each entry equal to either 0 or 1. Let mij denote the entry in row i and column j. A diago...
Let M be an n x n matrix with each entry equal to either 0 or 1. Let mij denote the entry in row i and column j. A diagonal entry is one of the form mii for some i. Swapping rows i and j of the matrix M denotes the following action: we swap the values mik and mjk for k = 1,2, ... , n. Swapping two columns is defined analogously. We say that M is rearrangeable if...
(6) (a) Consider the follow ing graph U T S 1] (ii) Does the graph have...
(6) (a) Consider the follow ing graph U T S 1] (ii) Does the graph have a closed Euler trail? If so, give an example of a closed Euler trail in 2] 1] (iv) Two identical looking bags are on a table. One cont ains 30 green marbles and 30 black marbles, and the other contains 10 green marbles, 10 blue marbles and 10 red marbles One of the bags is randomly selected (each has a 50% chance of being...
Write a menu based program implementing the following functions: (0) Write a function called displayMenu that...
Write a menu based program implementing the following functions: (0) Write a function called displayMenu that does not take any parameters, but returns an integer representing your user's menu choice. Your program's main function should only comprise of the following: a do/while loop with the displayMenu function call inside the loop body switch/case, or if/else if/ ... for handling the calls of the functions based on the menu choice selected in displayMenu. the do/while loop should always continue as long...
Problem 1 Write your code in the file MatrixOps.java. . Consider the following definitions from matrix...
Problem 1 Write your code in the file MatrixOps.java. . Consider the following definitions from matrix algebra: A vector is a one-dimensional set of numbers, such as [42 9 20]. The dot product of two equal-length vectors A and B is computed by multiplying the first entry of A by the first entry of B, the second entry of A by the second entry of B, etc., and then summing these products. For example, the dot product of [42 9...
Suppose the alphabet is sigma = {a, b, ..., z, 0, 1, ..., 9,: }, i.e., the standard letters a-z, decimal numbers, and colon (: ). The colon is used as a delimiter between fields in a text file. Each line of the file thus corresponds to a string. a) Give a regular expression that accepts strings with four fields (i.e., with 3 delimiters). b) Give a regular expression that accepts strings where the second field is numerical. c) Give...
6. (10 pts) Is L regular? Either prove that it is not regular using pumping lemma, or describe an RE for it. The alphabet of the language is 10,1, +,-) L = { x = y + z | x, y, z are binary integers, and x is the sum of y and z }. For example, strings 1000 = 101 + 11, 0101 = 010 + 11, and 101 = 101 + 0 are in the language, but strings...
1. Consider the alphabet {a,b,c}. Construct a finite automaton that accepts the language described by the following regular expression. 6* (ab U bc)(aa)* ccb* Which of the following strings are in the language: bccc, babbcaacc, cbcaaaaccbb, and bbbbaaaaccccbbb (Give reasons for why the string are or are not in the language). 2. Let G be a context free grammar in Chomsky normal form. Let w be a string produced by that grammar with W = n 1. Prove that the...
Let Σ = {0, 1). (a) Give a recursive definition of Σ., the set of strings from the alphabet Σ. (b) Prove that for every n E N there are 2" strings of length n in '. (c) Give a recursive definition of I(s), the length of a string s E Σ For a bitstring s, let O(s) and I(s) be number of zeroes and ones, respectively, that occur in s. So for example if s = 01001, then 0(s)...
Consider the language defined over the alphabet Σ (0, 1): [10] 2nin i. Show that L1 is context-free by specifying a CFG Gi for L1 ii. Convert the CFG Gi to a pushdown automaton Pv that accepts L1 by empty 12 stack iii. Give a pushdown automaton PF that accepts L by final state
(6) (a) Consider the follow ing graph U T S 1] (ii) Does the graph have a closed Euler trail? If so, give an example of a closed Euler trail in 2] 1] (iv) Two identical looking bags are on a table. One cont ains 30 green marbles and 30 black marbles, and the other contains 10 green marbles, 10 blue marbles and 10 red marbles One of the bags is randomly selected (each has a 50% chance of being...
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