Polynomial time algorithm - first order query, Mathematics

For queries Q1 and Q2, we say Q1 is contained in Q2, denoted Q1 ⊆ Q2, iff Q1 (D) ⊆ Q2(D) for every database D.

  • The container problem for a fixed Query Q0 is the following decision problem: Given a query Q, decide whether Q0 ⊆ Q.
  • The containee problem for a fixed query Q0 is the following decision problem: Given a query Q, decide whether Q ⊆ Q0.

Formally prove or disprove the following statements:

(a) For every conjunctive query Q0, there is a polynomial-time algorithm to decide the container problem for Q0 and for given conjunctive queries Q.

(b) For every conjunctive query Q0, there is a polynomial-time algorithm to decide the container problem for Q0 and for given conjunctive queries Q that can be obtained from Q0 by adding some atoms.

(c) For every conjunctive query Q0, there is a polynomial-time algorithm to decide the containee problem for Q0 and for given conjunctive queries Q.

(d) For every first-order Query Q0, there is an algorithm to decide the containee problem for Q0 and for given first-order queries Q. To prove a statement, sketch an algorithm, along with an argument why it is polynomial, if possible. To disprove it, provide an M-hardness or undecidability proof.

Posted Date: 3/1/2013 12:16:09 AM | Location : United States







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