Song Lyrics Program Plan: Define the class “SongLyrics”. Define the main method. Declare and initialize the string variable with song lyrics. Print the song lyrics.

Question

1.) Consider the problem of determining whether a DFA and a regular expression are equivalent. Express this problem as a language and show that it is decidable. ii) Let ALLDFA = {(A)| A is a DFA and L(A) = "}. Show that ALLDFA is decidable. iii) Let AECFG = {(G)| G is a CFG that generates &}. Show that AECFG is decidable. iv) Let ETM {(M)| M is a TM and L(M) = 0}. Show that ETM, the complement of Erm, is Turing-recognizable. Let X be the set {1, 2, 3, 4, 5} and Y be the set {6, 7, 8, 9, 10). We describe the functions f: XY and g: XY in the following tables. Answer each part and give a reason for each negative answer. n f(n) n g(n) 1 6 1 10 2 7 2 9 3 6 3 8 4 7 4 7 5 6 5 6 Aa. Is f one-to-one? b. Is fonto? c. Is fa correspondence? Ad. Is g one-to-one? e. Is g onto? f. Is g a correspondence? vi) Let B be the set of all infinite sequences over {0,1}. Show that B is uncountable using a proof by diagonalization.

Answer 1

Question

Chapter 1, Problem 6PE

Program Plan Intro

Song Lyrics

Program Plan:

Define the class “SongLyrics”.

Define the main method.

Declare and initialize the string variable with song lyrics.

Print the song lyrics.

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1.) Consider the problem of determining whether a DFA and a regular expression are equivalent. Express this problem as a language and show that it is decidable. ii) Let ALLDFA = {(A)| A is a DFA and L(A) = "}. Show that ALLDFA is decidable. iii) Let AECFG = {(G)| G is a CFG that generates &}. Show that AECFG is decidable. iv) Let ETM {(M)| M is a TM and L(M) = 0}. Show that ETM, the complement of Erm, is Turing-recognizable. Let X be the set {1, 2, 3, 4, 5} and Y be the set {6, 7, 8, 9, 10). We describe the functions f: XY and g: XY in the following tables. Answer each part and give a reason for each negative answer. n f(n) n g(n) 1 6 1 10 2 7 2 9 3 6 3 8 4 7 4 7 5 6 5 6 Aa. Is f one-to-one? b. Is fonto? c. Is fa correspondence? Ad. Is g one-to-one? e. Is g onto? f. Is g a correspondence? vi) Let B be the set of all infinite sequences over {0,1}. Show that B is uncountable using a proof by diagonalization.

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