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On the Complexity of Data Disjunctions
, 1999
"... We study the complexity of data disjunctions in disjunctive deductive databases (DDDBs), i.e., minimal clauses R(c 1 ) \Delta \Delta \Delta R(c k ), k 2, derived from the database in which all atoms involve the same predicate R. We consider deciding existence and uniqueness of a data disjunction ..."
Abstract

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We study the complexity of data disjunctions in disjunctive deductive databases (DDDBs), i.e., minimal clauses R(c 1 ) \Delta \Delta \Delta R(c k ), k 2, derived from the database in which all atoms involve the same predicate R. We consider deciding existence and uniqueness of a data disjunction, as well as actually computing one, both for propositional (data) and nonground (program) complexity of the database. Our results extend and complement previous results on the complexity of disjunctive databases, and provide tools for the analysis of the complexity of function computation using upgrading techniques, which we develop for this purpose.
Learning Weak Reductions to Sparse Sets
"... We study the consequences of NP having nonuniform polynomial size circuits of various types. We continue the work of Agrawal and Arvind [1] who study the consequences of Sat being manyone reducible to functions computable by nonuniform circuits consisting of a single weighted threshold gate. (Sa ..."
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We study the consequences of NP having nonuniform polynomial size circuits of various types. We continue the work of Agrawal and Arvind [1] who study the consequences of Sat being manyone reducible to functions computable by nonuniform circuits consisting of a single weighted threshold gate. (Sat ≤pm LT1). They claim that as a consequence P = NP follows, but unfortunately their proof was incorrect. We take up this question and use results from computational learning theory to show that if Sat ≤pm LT1 then PH = PNP. We furthermore show that if Sat disjunctive truthtable (or majority truthtable) reduces to a sparse set then Sat ≤pm LT1 and hence a collapse of PH to PNP also follows. Lastly we show several interesting consequences of Sat ≤pdtt SPARSE. 1
Learning Reductions to Sparse Sets
"... Abstract. We study the consequences of NP having nonuniform polynomial size circuits of various types. We continue the work of Agrawal and Arvind [1] who study the consequences of Sat being manyone reducible to functions computable by nonuniform circuits consisting of a single weighted threshold ..."
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Abstract. We study the consequences of NP having nonuniform polynomial size circuits of various types. We continue the work of Agrawal and Arvind [1] who study the consequences of Sat being manyone reducible to functions computable by nonuniform circuits consisting of a single weighted threshold gate. (Sat ≤ p m LT1). They claim that P = NP follows as a consequence, but unfortunately their proof was incorrect. We take up this question and use results from computational learning theory to show that if Sat ≤ p m LT1 then PH = P NP. We furthermore show that if Sat disjunctive truthtable (or majority truthtable) reduces to a sparse set then Sat ≤ p m LT1 and hence a collapse of PH to P NP also follows. Lastly we show several interesting consequences of Sat ≤ p dtt SPARSE.