Pushdown Systems with Stack Manipulation

Pushdown systems are a model of computation equipped with one stack where only the top of the stack is inspected and modified in each step of transitions. Although this is a natural restriction, some extensions of pushdown systems require more general operations on stack: conditional pushdown systems inspect the whole stack contents and discrete timed pushdown systems increment the ages of the whole stack contents. In this paper, we present a general framework called pushdown systems with transductions (TrPDS) for extending pushdown systems with transitions that modify the whole stack contents with a transducer. Although TrPDS is Turing complete, it is shown that if the closure of transductions appearing in the transitions of a TrPDS is finite, it can be simulated by an ordinary pushdown system and thus the reachability problem is decidable. Both of conditional and discrete timed pushdown systems can be considered as such subclasses of TrPDS.