6. Define a reset-PDA to be a PDA with an additional kind of transition that looks like this: 9 a, x reset r where a is an input symbol or and is a stack symbol or . The meaning of this transition is: read a from the input, pop x from the stack, reset the stack to the empty stack (e), and go to state r. Prove that every reset-PDA recognizes a context-free language, by showing how to convert a reset-PDA to a standard PDA (you don't need to prove the correctness of the construction). is the transition function. Here's a more formal definition, if you want it: a reset-PDA is a tuple P = (Q, E, I, 6, s, F), where Q, E, I, s, and F are as in a standard PDA, and 8: Q (EU {E}) (TU {e}) P(Q (TU {e, reset}))