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Title:
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The Plogi and ACi-1 operators on the polynomial time hierarchy
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Author:
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Castro Rabal, Jorge; Seara Ojea, Carlos
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Ciències de la Computació; Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. LARCA - Laboratori d'Algorísmia Relacional, Complexitat i Aprenentatge; Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta |
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Abstract:
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In a previous paper ([CS-92]) we studied the agreement of operators P_{log^i} and AC^{i-1} acting on NP. In this article we extend this work to other classes of the polynomial time hierarchy. We show that on Sigma_k^p, Pi_k^p, Delta_k^P and Theta_k^P-classes both operators have the same behaviour, but this coincidence does not seem to be true on other classes included in the PH hierarchy: we give a set A such that, relativized to A, P_{log^i}(P_{log^j}(NP)) is different from AC^{i-1}(P_{log^j}(NP)). As a result of these characterizations we show P_{log}(Theta_k^p) = Theta_k^p, an equality that is useful to show lowness properties. In fact, we get easily the Theta-lowness results given by Long and Sheu in their paper [LS-91]. Besides, we clarify the situation of the classes in L_2^{p,Delta} for which their membership to L_2^{p,Theta} was not clear. |
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Subject(s):
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-Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica
-Polynomial time hierarchy
-Operator agreement |
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Rights:
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Document type:
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Article - Published version
Report |
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