$\text{Definition:}$ A $\text{nondeterministic pushdown acceptor (npda)}$ is defined by the septuple
$M = (Q,\Sigma,\Gamma,\delta,q_0,z,F)$
where
$Q$ is a finite set of internal states of the control unit,
$\Sigma$ is the input alphabet,
$\Gamma$ is a finite set of symbols called the stack alphabet,
$\delta :Q\times(\Sigma\space \cup \{\lambda\})\times \Gamma \rightarrow$ set of finite subsets of $Q \times \Gamma^*$ is the transition function,
$q_0\in Q$ is the initial state of the control unit,
$z\in \Gamma$ is the $\text{stack start symbol, }$
$F\subseteq Q$ is the set of final states.
A two-stack automaton is a nondeterministic pushdown automaton with two independent stacks. To define such an automaton, we modify $\text{Definition}$ so that
$\delta: Q \times (\Sigma \cup \{\lambda\}) \times \Gamma \times \Gamma \rightarrow$ finite subsets of $Q\times \Gamma^* \times \Gamma^*$.
A move depends on the tops of the two stacks and results in new values being pushed on these two stacks. Show that the class of two-stack automata is equivalent to the class of Turing machines.
