1990
DOI: 10.1007/3-540-53414-8_44
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Hierarchies over the context-free languages

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Cited by 6 publications
(9 citation statements)
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“…Reinhardt [25] related the aforementioned hierarchy of his to another hierarchy defined by alternating pushdown automata and he gave a characterization of the polynomial hierarchy in terms of this alternating hierarchy using logarithmic-space (or log-space) many-one reductions. Using an argument similar to his, we can establish in Section 5 an exact characterization of the eth level of the Boolean hierarchy over the kth level Σ P k of the polynomial hierarchy in terms of the corresponding eth level of the Boolean hierarchy over the k + 1st level of the CFL hierarchy.…”
Section: Backgrounds and Main Themesmentioning
confidence: 99%
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“…Reinhardt [25] related the aforementioned hierarchy of his to another hierarchy defined by alternating pushdown automata and he gave a characterization of the polynomial hierarchy in terms of this alternating hierarchy using logarithmic-space (or log-space) many-one reductions. Using an argument similar to his, we can establish in Section 5 an exact characterization of the eth level of the Boolean hierarchy over the kth level Σ P k of the polynomial hierarchy in terms of the corresponding eth level of the Boolean hierarchy over the k + 1st level of the CFL hierarchy.…”
Section: Backgrounds and Main Themesmentioning
confidence: 99%
“…The many-one CFL hierarchy consists of language families Σ CFL m,k and Π CFL m,k (k ∈ N + ) defined as follows: Σ CFL m,1 = CFL, Π CFL m,k = co-Σ CFL m,k , and Σ CFL m,k+1 = CFL m (Π CFL m,k ) for any level k ≥ 1, where the subscript "m" stands for "many-one" as before. Relative to oracle A, a relativized many-one NFA hierarchy, which was essentially formulated in [25], is defined as follows: Σ NFA,A Since the proof of Theorem 4.12 is involved, prior to the proof, we intend to demonstrate how to prove Proposition 4.11 using this theorem.…”
Section: Structural Properties Of the Cfl Hierarchymentioning
confidence: 99%
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“…Related line of study concerns the types of reductions used in finite or pushdown automata with oracle. For example, nondeterministic finite automata with oracle complying with many-one restriction have been applied to establishing oracle hierarchies over the context-free languages [7]. For the same purpose, oracle pushdown automata have been used for many-one, truth-table, and Turing reducibil-ities, respectively, inducing the underlying definitions also to oracle nondeterministic finite automata [13].…”
Section: Introductionmentioning
confidence: 99%