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1.Remove redundant parentheses from the following expressions, that is, remove parentheses whose grouping would be implied by the precedence of operators and the fact that union and concatenation are each associative (and therefore, the grouping of adjacent unions or adjacent concatenations is irrelevant).
b) (a I (b(c)*)
c) (((a) I b)(c I d))
2.Put parentheses in the following regular expressions to indicate the proper grouping of operands according to the precedence of operators union, concatenation, and closure
a) a I bc I de
b) a I b * I (a I b)* a
3. Write regular expressions that define the following languages.
a) The set of all C identifiers that are not keywords. If you forget some of the keywords, it is not serious. The point of the exercise is to express strings that are not in some reasonably large set of strings.
b) All strings of a’s, b’s, and c’s such that no two consecutive positions are the same character
c) The set of all strings of two lower-case letters that are not the same. Hint: You can “brute-force” this one, but there are 650 pairs of distinct letters. A better idea is to do some grouping. For example, the relatively short expression covers 169 of the 650 pairs.
(a I b I ….. I m)(n I o I……..I z)
d) All strings of 0’s and 1’s that, as a binary number, represent an integer that is a multiple of 3
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4. Write regular expressions that define the following languages.
a) The strings for the six C comparison operators, =, <=, =, >, and !=.
b) All strings of 0’s and 1’s that end in 0.
c) All strings of 0’s and 1’s with at least one 1.
d) All strings of 0’s and 1’s with at most one 1.
e) All strings of 0’s and 1’s such that the third position from the right end is 1.
f) All strings of lower-case letters that are in sorted order.
5.In Example 10.13 we considered the regular expression (a | ab) (c | bc), and saw that its language consisted of the three strings ac, abc, and abbc, that is, an a and ac, separated by from zero to two b’s. Write two other regular expressions that define the same language.
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