IDPDA

Other names: Visibly pushdown automata, nested word automat.

A subclass of deterministic pushdown automata called input-driven pushdown automata (IDPDA), in which the input symbol determines whether the automaton should push a stack symbol, pop a stack symbol or leave the stack untouched, was introduced by Mehlhorn

— State complexity of operations on input-driven pushdown automata, 2017

Visibly pushdown automata (VPA), also known as input-driven pushdown automata, are a subclass of pushdown automata, in which the type of stack operation is determined by the input letter [33, 4]. This implies that the stack height, but not its content, is determined by the input word. This enables the construction of the product VPA from two given VPA. In consequence, the class of visibly pushdown languages recognized by VPA is closed under intersection, union and complement, which makes the universality problem decidable.

— Learning Deterministic Visibly Pushdown Automata Under Accessible Stack