Suppose we're given the non-deterministic PDA shown below which reads from the alphabet $\sum = \lbrace a,b \rbrace$. How will this PDA behave if we pass it the string $ba$? We read $b$ first and push $b$ to the stack, but when we read $a$ I get confused. My assumption is that we fork into two new branches - one in which $b$ was popped and one in which $a$ was pushed. Is this correct? If not, can you tell me where I go wrong?
Thank you very much!