We studied in class that PDA is less powerful than TM.
My question is:
Extended PDA : for every $\alpha,\beta \in \Gamma \cup \{\epsilon\}$, $\sigma \in \Sigma \cup \{\epsilon\}$, $q,r \in Q$, $w \in \Sigma^*$,$\gamma \in \Gamma^*$:
if $(q,b) \in \Delta(r,\sigma,\alpha,\mathrm{up})$ than $(r,\sigma w, \alpha \gamma) \to (q,w,\beta \gamma)$ and if $(q,b) \in \Delta(r,\sigma,\alpha,\mathrm{down})$ than $(r,\sigma w, \gamma \alpha ) \to (q,w,\gamma \beta)$ is equivalent to TM?
I think that it's correct, because extended PDA can implement a queue automaton which is equivalent to TM.