Linearising nonlinear recursions in polynomial time

  • Authors:
  • Y. P. Saraiya

  • Affiliations:
  • Department of Computer Science, Stanford University

  • Venue:
  • PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
  • Year:
  • 1989

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Abstract

The replacement of nonlinear recursions with equivalent linear recursions is a potentially useful query optimization strategy, since it permits the use of efficient algorithms for the evaluation of linear logic programs. We show that a member of a certain class of bilinear recursions is linearizable in a strong sense if and only if a specific partial proof tree derived from this recursion is contained in a bounded number of partial proof trees generated by the recursion. Further, while each such test of containment between proof trees involves an exponential number of conjunctive-query containment tests, we present syntactic conditions on the recursion that are necessary and sufficient for the containment and verifiable in polynomial time.