What is the computational class of a pushdown automaton with real values? Say there is a push-down automata, in this example I'll use a deadfish-like set:
+: increase x by 1
0: set x to 0
ln: set x to ln(x) &lt;-- real valued result
With x being an infinite precision real-valued variable, does this allow said machine to have more power than if it was operating on integers? Or am I misunderstanding something?
Since none of your instructions can influence the behavior of the pushdown automaton (they can only influence the value of $x$), this does not change which languages the pushdown automaton can accept.