The set of words that begin with two $a$s, which are followed by any positive number of $b$s, which are followed by more $c$s than there are $b$s. The last line of the transition table allows us to read any number of $c$s now, staying in state $q_4$ with the stack empty. In state $q_3$ all we can do is read $c$s, popping a $B$ off the stack each time, until the stack is empty, at which point the transition $d(q_3,c,Z)=(q_4,Z)$ allows us to read one more $c$ and move to state $q_4$ with the stack empty. Reading a $c$ pops one $B$ off the stack, and $M$ goes to state $q_3$. Eventually, however, we need an input of $c$ to get out of $q_2$, but since there is no transition for an input of $c$ to state $q_2$ when the stack is empty, we do need to have read in at least one $b$ first. The transitions $d(q_2,b,Z)=(q_2,BZ)$ and $d(q_2,b,B)=(q_2,BB)$ allow $M$ to read $n$ $b$s and place $n$ $B$s on the stack, remaining in state $q_2$ the whole time. After that second $a$ is read, $M$ is in state $q_2$, and the stack is still empty. Again there is only one transition available, so the next character must also be an $a$ if the word is to have any hope of being accepted.
The automatons can be accessed after completing The World Wakes and the other required quests. When that $a$ is read, the stack remains empty, but $M$ moves to state $q_1$. Automaton Tracers drop the rare and expensive pneumatic gloves, currently worth 212,184, in addition to very good regular drops of herbs, seeds, and raw materials. Notice that there is only one possible transition from the initial state $q_0$, so any word that is accepted must start with $a$. You can be pretty sure that your answer to (ii) is wrong, since (iii) asks you to show that $aabbccc\in L(M)$, and $aabbccc$ doesn’t satisfy the condition in your answer to (ii). I believe I did something wrong with B or kept repeating B in every trace. Ii) The PDA M accepts strings that have abc as a substring (not sure) (iii) Show that aabbccc is in L(M) by tracing the computation of M on this input described in terms of configurations and the relation "|-". Notes: They have a special attack where they smash their fists into the ground. (i) Formally define M by listing all its elements using the definition of d and the assumption that: q0 is the start state and q4 is the only final state of M. The Automaton Tracer is found in the third chamber of the ruins during the World Wakes quest.
Z is the bottom of the stack symbol and e denotes the empty string. Let M be a deterministic PDA with the transition function d: d(q0,a,Z)= (q1,Z)