Answer:
a[ab]*b
a[ab]*b
Consider the set of strings of any length with an equal number of 'a' and 'b' arranged in any manner.
Accepted:
Ø, ab, ba, aabb, abab, bbaa, abba, aaabbb, bbbaaa, ababab, abaabb, ... aaaabbbb, bbbbaaaa, abababab, aabbaabb, abaaabbb, ...
But Not:
a, b, aa, bb, abb, bba, aba, bbb, aaa, ... aaabbbb, aaabbbbb, bbbbbbba, ...
(Thought question: ) Can this pattern be expressed with a RE? Can you design a finite automaton that accepts this language?