如何找到所有大于 110011 的二进制数的正则表达式

Question

I am trying to solve a problem set to practice for an exam. How can I approach questions like these? Is there a way to verify solutions or is it just trial and error?

Answer 1

This one seems quite simple: the string has to be one of:

• 1 followed by at least six more characters.
• 111 followed by at least (or exactly) three characters
• 1111 followed by at least (or exactly) two characters.

If the input can start with leading 0s, change all the leading "1"s to "0*1". In any case, it can be factored out.

The answer to your question, "is there a simple algorithm which can do that for me?" is probably "no". But the above is more simple logic than trial-and-error. Writing down random regular expressions until you find one which works is not a good way to solve the problem, given the difficulty of algorithmically proving correctness.