Efficient Read-Restricted Monotone CNF/DNF Dualization by Learning with Membership Queries
We consider exact learning monotone CNF formulas in which each variable appears at most some constant k times ("read-k" monotone CNF). Let f : {0,1}^sup n^ [arrow right] {0,1} be expressible as a read-k monotone CNF formula for some natural number k. We give an incremental output polynomia...
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| Published in: | Machine learning Vol. 37; no. 1; pp. 89 - 110 |
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| Language: | English |
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01.10.1999
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| ISSN: | 0885-6125, 1573-0565 |
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| Abstract | We consider exact learning monotone CNF formulas in which each variable appears at most some constant k times ("read-k" monotone CNF). Let f : {0,1}^sup n^ [arrow right] {0,1} be expressible as a read-k monotone CNF formula for some natural number k. We give an incremental output polynomial time algorithm for exact learning both the read-k CNF and (not necessarily read restricted) 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}^sup n^. The algorithm yields an incremental polynomial output time solution to the (read-k) monotone CNF/DNF dualization problem. The unrestricted versions remain open problems of importance.[PUBLICATION ABSTRACT] |
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| AbstractList | We consider exact learning monotone CNF formulas in which each variable appears at most some constant k times (`read-k' monotone CNF). Let f: {0,1} super(n) arrow right {0,1} be expressible as a read-k monotone CNF formula for some natural number k. We give an incremental output polynomial time algorithm for exact learning both the read-k CNF and (not necessarily read restricted) 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 xIMOS{0,1} super(N). The algorithm yields an incremental polynomial output time solution to the (read-k) monotone CNF/DNF dualization problem. The unrestricted versions remain open problems of importance. We consider exact learning monotone CNF formulas in which each variable appears at most some constant k times ("read-k" monotone CNF). Let f : {0,1}^sup n^ [arrow right] {0,1} be expressible as a read-k monotone CNF formula for some natural number k. We give an incremental output polynomial time algorithm for exact learning both the read-k CNF and (not necessarily read restricted) 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}^sup n^. The algorithm yields an incremental polynomial output time solution to the (read-k) monotone CNF/DNF dualization problem. The unrestricted versions remain open problems of importance.[PUBLICATION ABSTRACT] |
| Author | Mishra, Nina Pitt, Leonard Domingo, Carlos |
| Author_xml | – sequence: 1 givenname: Carlos surname: Domingo fullname: Domingo, Carlos – sequence: 2 givenname: Nina surname: Mishra fullname: Mishra, Nina – sequence: 3 givenname: Leonard surname: Pitt fullname: Pitt, Leonard |
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| Title | Efficient Read-Restricted Monotone CNF/DNF Dualization by Learning with Membership Queries |
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