Two ways of introducing alternation into context-free grammars and pushdown automata

Two ways of introducing alternation for context-free grammars and pushdown automata are compared. One is the usual way which combines "states" with alternation [1], [4], [7], and the other is the way used in [6] to define the alternating context-free grammar, i.e., alternation is governed by the variables of the grammar. In this paper the latter way is taken over to define a new type of alternating pushdown automaton by combining the "pushdown symbols" of the pushdown automaton with alternation. We have derived a characterization of the original alternating context-free grammars in terms of such a new type of alternating pushdown automaton without states. It is also shown that, if (non-alternating) states are introduced as an additional feature for this type of pushdown automaton, then the resulting alternating pushdown automaton has exactly the same expressive power as the original alternating pushdown automaton.