Discovery and Deduction

  • Authors:
  • Masami Hagiya;Koichi Tagahashi

  • Affiliations:
  • -;-

  • Venue:
  • DS '00 Proceedings of the Third International Conference on Discovery Science
  • Year:
  • 2000

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Abstract

Deduction is usually considered to be the opposite of induction. However, deduction and induction can be related in many ways. In this paper, two endeavors that try to relate discovery science and verification technology are described. The first is discovery by deduction, where attempts to find algorithms are made using verifiers. Case studies of finding algorithms for concurrent garbage collection and for mutual exclusion without semaphores are described. Superoptimization can also be classified as work in this field. Recent work on finding authentication protocols using a protocol verifier is also briefly surveyed. The second endeavor is discovery for deduction. This concerns the long-standing problem of finding induction formulae or loop invariants. The problem is regarded as one of learning from positive data, and the notion of safe generalization, which is commonly recognized in learning from positive data, is introduced into iterative computation of loop invariants. The similarity between the widening operator in abstract interpretation and Gold's notion of identification in the limit is also discussed.