Efficient Read-Restricted Monotone CNF/DNF Dualization by Learning with Membership Queries

  • Authors:

  • Carlos Domingo;Nina Mishra;Leonard Pitt

  • Affiliations:

  • Department of Mathematical and Computing Science, Tokyo Institute of Technology, Meguro-ku, Ookayama, 152-8522 Tokyo, Japan. carlos@is.titech.ac.jp;Hewlett-Packard Laboratories, 1501 Page Mill Rd, MS1U-4A, Palo Alto, CA 94304. nmishra@hpl.hp.com;Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL 61801. pitt@cs.uiuc.edu

  • Venue:
  • Machine Learning
  • Year:
  • 1999

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Abstract

We consider exact learning monotone CNF formulas in whicheach variable appears at most some constant k times(“read-k” monotone CNF). Let f : {0,1}^n → {0,1}be expressible as a read-k monotone CNF formula for some naturalnumber k. We give an incremental output polynomial time algorithm for exact learning both the read-k CNF and (not necessarily readrestricted) DNF descriptions of f. The algorithm‘s only method of obtaining information about f is through membership queries, i.e., by inquiring about the value f(x) for points x ∈ {0,1}^n. The algorithm yields an incremental polynomial output timesolution to the (read-k) monotone CNF/DNF dualization problem. The unrestricted versions remain open problems of importance.