Abstract. This paper presents a unified solution to the problem of extending stratified DATALOG to express database complexity classes ranging from P to QH; QH is the query hierarchy containing the decision problems that can be solved in polynomial time by a deterministic Turing machine using a constant number of calls to an NP-oracle. The solution is based on (i) stratified negation as the core of a simple, declarative semantics for negation, (ii) the use of a “choice ” construct to capture the nondeterminism of stable models in a disciplined fashion, (iii) the ability to bind a query to the lowest complexity level that includes the problem at hand, and (iv) a general algorithm that adapts its behavior to the desired level of complexity required by the query so that exponential time computation is only required for hard problems. 1
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D.: Complexity and Expressive Power of Deterministic Semantics for DATALOG
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1
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DB-N P this paper ∃Q ¬ DB-N P [24] ∀Q ¬ DB-coN P [24, 35] ∃∀Q ¬ DB-D p [31] !Q ¬s,c DB-P this paper ∃Q ¬s,c DB-N P this paper ∀Q ¬s,c DB-coN P this paper ∃∀Q ¬s,c DB-coN P this paper
– unknown authors
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1
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s,c DB-QH this paper
– unknown authors
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