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Select all strings matched by the regular expression1*0(11*00*)*0*11 pointε1011110011111110111000000110101011010111

Question

Select all strings matched by the regular expression 1*0(11*00*)*0*11

pointε 1011110011111110111000000110101011010111

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Solution

The regular expression 1*0(11*00*)*0*11 can be broken down as follows:

  • 1* matches zero or more occurrences of 1.
  • 0 matches exactly one occurrence of 0.
  • (11*00*)* matches zero or more occurrences of the pattern 11*00*. This pattern itself can be broken down into:
    • 11* matches one 1 followed by zero or more 1s.
    • 00* matches one 0 followed by zero or more 0s.
  • 0* matches zero or more occurrences of 0.
  • 11 matches exactly two occurrences of 1.

Given the string ε1011110011111110111000000110101011010111, let's find all substrings that match the regular expression:

  1. 1011110011: This string starts with one or more 1s, followed by a 0, then the pattern 11*00* twice (i.e., 11 followed by 00, and then 11 followed by 00), and ends with 11.

  2. 1011110011111110111: This string starts with one or more 1s, followed by a 0, then the pattern 11*00* three times (i.e., 11 followed by 00, 11 followed by 00, and 11 followed by 00), and ends with 11.

  3. 101111001111111011100000011: This string starts with one or more 1s, followed by a 0, then the pattern 11*00* four times (i.e., 11 followed by 00, 11 followed by 00, 11 followed by 00, and 11 followed by 00), and ends with 11.

So, the strings matched by the regular expression 1*0(11*00*)*0*11 in the given string are 1011110011, 1011110011111110111, and 101111001111111011100000011.

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