Write a regular expression over the given language. [closed]

automata regular-expressions

Words in $L$ can be divided into length-$2$ blocks, an odd number of which are $ab$ or $ba$ (for they change the parity of the $b$ count and $aa,bb$ don't). Letting $X=(aa|bb)^*$ and $Y=(ab|ba)$, a regular expression for $L$ is $X(YXYX)^*YX$.

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