The article discusses the use of various types of queries in concept learning, including membership, equivalence, subset, superset, disjointness, and exhaustiveness queries. It explores how these queries can be used to efficiently learn unknown concepts, particularly in formal domains such as regular languages, context-free languages, and propositional formulas. The paper also compares equivalence queries with Valiant's criterion of probably approximately correct (PAC) identification under random sampling.
Key findings include the necessity of a certain number of queries for exact identification in various domains, such as the need for up to $2^n - 1$ queries in the case of 1-CNF or 1-DNF formulas. The paper also presents algorithms for exact identification using equivalence and membership queries, such as the majority vote strategy for $k$-CNF formulas. Additionally, it discusses the use of subset and superset queries in identifying pattern languages and the role of disjointness queries in debugging Prolog programs. The paper concludes with a lower bound for all six query types, demonstrating that $N - 1$ queries are necessary for certain domains, even with the full set of query types.The article discusses the use of various types of queries in concept learning, including membership, equivalence, subset, superset, disjointness, and exhaustiveness queries. It explores how these queries can be used to efficiently learn unknown concepts, particularly in formal domains such as regular languages, context-free languages, and propositional formulas. The paper also compares equivalence queries with Valiant's criterion of probably approximately correct (PAC) identification under random sampling.
Key findings include the necessity of a certain number of queries for exact identification in various domains, such as the need for up to $2^n - 1$ queries in the case of 1-CNF or 1-DNF formulas. The paper also presents algorithms for exact identification using equivalence and membership queries, such as the majority vote strategy for $k$-CNF formulas. Additionally, it discusses the use of subset and superset queries in identifying pattern languages and the role of disjointness queries in debugging Prolog programs. The paper concludes with a lower bound for all six query types, demonstrating that $N - 1$ queries are necessary for certain domains, even with the full set of query types.