FLAT

Regular expression for string starts and ends with same character

Convert from NFA to DFA using Thompson’s rule for (a+b)*abb

1. 0(0+1)*0

  • This regular expression matches any string that starts and ends with 0.
  • Breakdown:
    • The first 0 ensures the string starts with 0.
    • (0+1)* means the middle part of the string can be any combination of 0s and 1s (zero or more occurrences of 0 or 1).
    • The final 0 ensures the string ends with 0.

2. 1(0+1)*1

  • This regular expression matches any string that starts and ends with 1.
  • Breakdown:
    • The first 1 ensures the string starts with 1.
    • (0+1)* means the middle part of the string can be any combination of 0s and 1s (zero or more occurrences).
    • The final 1 ensures the string ends with 1.

3. a(a+b)*a

  • This regular expression matches any string that starts and ends with a.
  • Breakdown:
    • The first a ensures the string starts with a.
    • (a+b)* allows the middle part of the string to be any combination of as and bs.
    • The final a ensures the string ends with a.

4. b(a+b)*b

  • This regular expression matches any string that starts and ends with b.
  • Breakdown:
    • The first b ensures the string starts with b.
    • (a+b)* allows the middle part of the string to be any combination of as and bs.
    • The final b ensures the string ends with b.
 

 

  • The basic structure of these regular expressions is that they specify the first and last character of the string, which must be the same, and allow any combination of characters in between.
  • (0+1)* or (a+b)* represents a pattern where either character (from the given set) can appear zero or more times between the first and last character.

These regular expressions can be adjusted to any specific character set by modifying the starting and ending characters along with the middle expression.

 

 
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Convert from NFA to DFA using Thompson’s rule for (a+b)*abb
FLAT

Prove that L = {ww | w ∈ {0, 1}∗} is not regular

Assume that L is regular. Let p be the pumping length guaranteed by the Pumping Lemma. Take w =0p10p1 .