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Chapter 0: Q5E (page 26)
If is a set withelements, how many elements are in the power set of ? Explain your answer.
The number of elements in the power set of is elements.
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Give informal English descriptions of PDAs for the languages in Exercise 2.6
Give context-free grammars generating the following languages.
a. The set of strings over the alphabet with more a's than b's
b. The complement of the language .
c. is a substring of x for w,x
d. localid="1662105288591" each xilocalid="1662105304877" and for some i and j ,localid="1662105320570"
Show thatif,.then
Let Give a CFG generating the language of strings with twice as many . Prove that your grammar is correct.
Let F be the language of all strings over that do not contain a pair of 1s that are separated by an odd number of symbols. Give the state diagram of a DFA with five states that recognizes . (You may find it helpful first to find a 4-state NFA for the complement of ).
Question: 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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