patternMinor
Does $L_1L_2 = L_2L_1$ imply $L_1 = L_2$?
Viewed 0 times
l_1l_2implyl_1doesl_2l_2l_1
Problem
Let $L_1, L_2 \subseteq \Sigma^*$ be two languages, where $\Sigma$ is some finite Alphabet.
Does $L_1L_2 = L_2L_1$ imply $L_1 = L_2$?
What if $L_1$ and $L_2$ are regular languages?
Can you give counterexamples?
Does $L_1L_2 = L_2L_1$ imply $L_1 = L_2$?
What if $L_1$ and $L_2$ are regular languages?
Can you give counterexamples?
Solution
No, just take as counter example $L_1=\epsilon$ and $L_2$ any other langage different from $L_1$.
Context
StackExchange Computer Science Q#109771, answer score: 6
Revisions (0)
No revisions yet.