Name
Abstract | ||
|---|---|---|
As a natural extension of the SAT problem, an array of proof systems for quantified Boolean formulas (QBF) have been proposed, many of which extend a propositional proof system to handle universal quantification. By formalising the construction of the QBF proof system obtained from a propositional proof system by adding universal reduction (Beyersdorff, Bonacina u0026 Chew, ITCSu002716), we present a new technique for proving proof-size lower bounds in these systems. The technique relies only on two semantic measures: the cost of a QBF, and the capacity of a proof. By examining the capacity of proofs in several QBF systems, we are able to use the technique to obtain lower bounds based on cost alone. As applications of the technique, we first prove exponential lower bounds for a new family of simple QBFs representing equality. The main application is in proving exponential lower bounds with high probability for a class of randomly generated QBFs, the first u0027genuineu0027 lower bounds of this kind, which apply to the QBF analogues of resolution, Cutting Planes, and Polynomial Calculus. Finally, we employ the technique to give a simple proof of hardness for a prominent family of QBFs. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.4230/LIPIcs.ITCS.2018.9 | conference on innovations in theoretical computer science |
DocType | Volume | Citations |
Conference | 94 | 1 |
PageRank | References | Authors |
0.39 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Olaf Beyersdorff | 1 | 223 | 30.33 |
| Joshua Blinkhorn | 2 | 3 | 6.16 |
| Luke Hinde | 3 | 1 | 1.06 |