Q7

Construct as minimal finite state machine that accepts the language, over $\{0,1\}$, of all strings that contain neither the substring $00$ nor the substring $11$.

Consider the grammar $S \to aSAb$ $S \to \epsilon$ $A \to bA$ $A \to \epsilon$ where $S$, $A$ are non-terminal symbols with $S$ being the start symbol; $a, b$ are terminal symbols and $\epsilon$ is the empty string. This grammar generates strings of the form $a^ib^j$ for some $i, j \geq 0$, where $i$ and $j$ satisfy some condition. What is the condition on the values of $i$ and $j$?