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Chapter 0: Q20E (page 1)

For each of the following languages, give two strings that are members and two strings that are not members鈥攁 total of four strings for each part. Assume the 危=a,balpha-alphabet in all parts.

a.a*b*b.aba*bc.a*鈭�b*d.aaa*e.危*a危*b危*a危*f.aba鈭�babg.(蔚鈭�a)bh.(a鈭�ba鈭�bb)危*

Short Answer

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Step by step solution

01

To Concern the Two Strings

There are two strings which are concerned with members, and some of the two strings are concerned with non-members. In the question, there are some calculations we have to solve, and they're related to the step-2 answer also.

02

To Explain the Given Expression

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Most popular questions from this chapter

Question: Each of the following languages is the complement of a simpler language. In each part, construct a DFA for the simpler language, and then use it to give the state diagram of a DFA for the language given. In all parts, 危=a,b.

a.w|wdoesnotcontainthesubstringabAb.{w|wdoesnotcontainthesubstringbaba}c.{w|wcontainsneitherthesubstringsabnorba}d.{w|wisanystringnotina*b*}e.{w|wisanystringnotin(ab+)*}f.{w|wisanystringnotina*鈭�b*}g.{w|wisanystringthatdoesntcontainexactlytwoas}h.{w|wisanystringexceptaandb}

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 a,bwith more a's than b's

b. The complement of the language anbnn鈮�0.

c. w#xwRis a substring of x for w,x 鈭�0,1*

d. localid="1662105288591" x1#x2#...#xkk鈮�1,each xilocalid="1662105304877" 鈭�a,b*,and for some i and j ,localid="1662105320570" xi=xjR

Let D=w|wcontains an even number of 鈥檚 and an odd number of 鈥檚 and does not contain the substring ab}. Give a DFA with five states that recognizes Dand a regular expression that generates D.(Suggestion: Describe Dmore simply.)

Use the construction given in Theorem 1.39 to convert the following two nondeterministic finite automata to equivalent deterministic finite automata.

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.
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