# Exact Learning of Subclasses of CDNF Formulas with Membership Queries

@inproceedings{Domingo1996ExactLO, title={Exact Learning of Subclasses of CDNF Formulas with Membership Queries}, author={Carlos Domingo}, booktitle={International Computing and Combinatorics Conference}, year={1996} }

We consider the exact, learuability of subclasses of Boolean formulas from membership queries alone. We show how to combine known learning algorithms that use membership and equivalence queries to obtain new learning results only with memberships. In particular we show the exact learuability of read-k monotone formulas, Sat-k\(\mathcal{O}\)(log n)-CDNF, and \(\mathcal{O}(\sqrt {\log n} )\)-size CDNF from membership queries only.

## 3 Citations

### Exact Learning from an Honest Teacher That Answers Membership Queries

- Computer Science, MathematicsTheor. Comput. Sci.
- 2018

### Computational aspects of monotone dualization: A brief survey

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- 2008

### Polynominal Time Algorithms for Some Self-Duality Problems

- Mathematics, Computer ScienceCIAC
- 1997

This paper exhibits polynomial time algorithms for testing self-duality for several natural classes of formulas where the problem was not known to be solvable.

## References

SHOWING 1-10 OF 28 REFERENCES

### Read-thrice DNF is hard to learn with membership and equivalence queries

- Computer ScienceProceedings., 33rd Annual Symposium on Foundations of Computer Science
- 1992

It is shown that, assuming NP not=co-NP, there does not exist a polynomial-time membership and equivalence query algorithm for exactly learning read-thrice DNF formulas-boolean formulas in disjunctive normal form where each variable appears at most three times.

### Exact learning of read-twice DNF formulas

- Computer Science[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science
- 1991

A polynomial-time algorithm is presented for exactly learning the class of read-twice DNF formulas, i.e. Boolean formulas in disjunctive normal form where each variable appears at most twice. The…

### How many queries are needed to learn?

- Computer Science, MathematicsJACM
- 1996

It is shown that an honest class is exactly polynomial-query learnable if and only if it is learnable using an oracle for Γp4, and a new relationship between query complexity and time complexity in exact learning is shown.

### Exact Learning Boolean Function via the Monotone Theory

- Computer Science, MathematicsInf. Comput.
- 1995

The Monotone Theory is developed that proves (1) Any boolean function is learnable in polynomial time in its minimal disjunctive normal form size, its minimal conjunctive normalform size, and the number of variables n, and (2) Decision trees are learnable.

### When won't membership queries help?

- Computer Science, MathematicsSTOC '91
- 1991

We investigate cryptographic limitations on the power of membership queries to help with concept learning. We extend the notion of prediction-preserving reductions to prediction with membership…

### Oracles and queries that are sufficient for exact learning (extended abstract)

- Computer Science, MathematicsCOLT '94
- 1994

There is a randomized polynomial-time algorithm that learns any class that is learnable from membership queries with unlimited computational power.

### Read-Twice DNF Formulas are Properly Learnable

- Computer ScienceInf. Comput.
- 1993

We show that read-twice DNF formulas-Boolean formulas in disjunctive normal form in which each variable appears at most twice-are exactly and properly learnable in polynomial time. Our algorithm uses…

### Learning Monotone Term Decision Lists

- Computer ScienceEuroCOLT
- 1997

It is shown that, for any constant k≥0, k-term monotone decision lists are exactly and properly learnable with nO(k) membership queries in O(nk3) time.

### Learning read-once formulas with queries

- Mathematics, Computer ScienceJACM
- 1993

The main results are a polynomial-time algorithm for exact identification of monotone read-once formulas using only membership queries, and a protocol based on the notion of a minimally adequate teacher using equivalence and membership queries.