Deciding Equivalence of Deterministic Pushdown Automata

Deterministic pushdown automata (DPDA) are a class of simple yet powerful models of computation. It has a finite set of states and a (pushdown) stack. Depending on the current state, the symbol at the top of the stack, and the symbol of the input word that has just been scanned, the automaton moves to a new state, either pushes or pops a symbol on the stack, and it is ready to scan the next symbol of the input word. If a distinguished state, called accepting, is reached just when the entire word has been scanned, the input word is said to be recognized by the automaton. DPDAs are standardly used as a device to define sets of words, called languages. For a good introduction to pushdown automata (and Automata Theory in general), I recommend [4] or [9].