A grammatical characterization of alternating pushdown automata

On Alternating Phrase-Structure Grammars

“…In [12] an alternating context-free grammar is defined as G = (V, U, Σ, P, S), where V is a finite set of variables (or nonterminals), U ⊆ V is a set of universal variables, while the variables in V U are called existential, Σ is a finite set of terminals, S is the start symbol, and P is a finite set of context-free productions. In the derivation process an existential variable is rewritten as usual, but a universal variable is rewritten by applying all productions with that variable as left-hand side simul-taneously, thus giving a finite number of successor sentential forms.…”

“…Observe thatȦ e andȦ u are both existential variables of G . Next the index e or u is moved to the right using productions (2) to (14). In this process the variableȦ e orȦ u is replaced by the variable e or A u , respectively, which are both existential.…”

“…In [12] one of the present authors introduced the concept of alternation for context-free grammars by defining the so-called alternating context-free grammars (ACFG for short). In these grammars one distinguishes between existential and universal variables (nonterminals).…”

“…However, no such characterization was obtained in [12], and as a consequence further studies of the notion of alternation for context-free grammars and pushdown automata followed (see, e.g., [6,13,14,15]). In fact, also Okhotin's conjunctive grammars [17] can be interpreted as a variant of ACFGs in which the effect of universal steps is localized.…”

Alternating Finite Automata with Limited Universal Branching

“…Deterministic and nondeterministic finite automata (DFA and NFA) are well understood models for which a significant number of results are known. As a generalization of nondeterminism, alternation was introduced in [1], and has since been studied extensively for Turing machines [5,6,23], and pushdown automata [1,20].…”