More theory revision with queries (extended abstract)

Abstract

Given a Boolean formula that is not quite right, how does one fix it? That is, if a given formula differs from an unknown target formula, what is the complexity of revising the given formula? The tools available for determining the revisions are queries to membership and equivalence oracles, namely, questions of the form: "Is this an instance of the target formula," and "Is this hypothesis equivalent to the target formula?" In the latter case, if the answer is "No," the oracle returns an instance that is true for exactly one of the hypothesis and the target. For Horn sentences that require only deletion revisions, a revision algorithm is given that is polynomial in the number of clauses of the formula and the minimum number of deletions needed. For 2-term monotone DNF formulas, a revision algorithm is given that is polynomial in the minimum number of necessary deletions and additions and the logarithm of the number of variables. Previous work addressed deletion-only revisions to 2-term unate DNF formulas.

Theory revision with queries: Horn, read-once, and parity formulas

“…Preliminary versions of many of the results in this paper appeared in the three conference papers [28,29,50], and in a master's thesis of the third author [51].…”