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.

The alternating variant of the shrinking two-pushdown automaton of Buntrock and Otto (1998) is introduced. It is shown that the class of languages accepted by these automata is contained in the class of deterministic context-sensitive languages, and that it contains a PSPACE-complete language. Hence, the closure of this class of languages under log-space reductions coincides with the complexity class PSPACE.

As a generalization of the tree automaton, tree automata with various types of memory are introduced and their relation to context-free grammars with memory is studied. Relations between computation trees of tree automata with memory and derivation trees of context-free grammars with memory are established, and as a consequence, the languages generated by context-free grammars with memory are characterized in terms of the sets of trees recognizable by tree automata with memory. Also various types of traversal of labeled trees recognizable by tree automata with memory are considered.

CFGs (context-free grammars) with various types of memory are introduced and their generative capacities are investigated. For an automata-theoretic characterization, a new type of automaton called partitioning automaton is introduced and it is shown that the class of languages generated by CFGs with memory type X is equal to the class of languages accepted by partitioning automata of type X.