1989
DOI: 10.1016/0304-3975(89)90023-6
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A grammatical characterization of alternating pushdown automata

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Cited by 14 publications
(5 citation statements)
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“…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.…”
Section: Alternating Grammarsmentioning
confidence: 99%
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“…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.…”
Section: Alternating Grammarsmentioning
confidence: 99%
“…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.…”
Section: Propositionmentioning
confidence: 99%
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“…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].…”
Section: Introductionmentioning
confidence: 99%