Question

Write a regular expression that describes the following statements where ∑ = {0, 1}:

a) All strings that do not contain the substring 01.
b) Every 1 is immediately followed by 00.
c) All string starting with 0 but not having consecutive 1's. 2.

Answer 1

The student's regular expression questions pertain to constructing patterns for string sets within a binary alphabet, each matching specific criteria related to the arrangement of zeros and ones. This includes avoiding a specific substring, ensuring a particular sequence after a character, and starting with a certain character without consecutive occurrences of another.

Step-by-step explanation:

The student's question involves constructing regular expressions for a series of different string specifications within an alphabet Σ = {0, 1}. The requirements are:

• a) All strings that do not contain the substring 01 can be described by the regular expression (0*|11*)*. This regular expression allows any number of 0s or any number of 1s in sequence, but not the combination 01.
• b) For strings where every '1' is immediately followed by '00', the regular expression is (0|100)*. This ensures that a 1, if present, is always followed by two 0s, while 0s can appear freely.
• c) All strings starting with 0 but not having consecutive 1s can be represented by the regular expression 0(0|10)*. This expression starts with a 0 and follows with any number of 0s or single 1s followed by a 0.