QBF Merge Resolution is powerful but unnatural

05/26/2022
by   Meena Mahajan, et al.
0

The Merge Resolution proof system (M-Res) for QBFs, proposed by Beyersdorff et al. in 2019, explicitly builds partial strategies inside refutations. The original motivation for this approach was to overcome the limitations encountered in long-distance Q-Resolution proof system (LD-Q-Res), where the syntactic side-conditions, while prohibiting all unsound resolutions, also end up prohibiting some sound resolutions. However, while the advantage of M-Res over many other resolution-based QBF proof systems was already demonstrated, a comparison with LD-Q-Res itself had remained open. In this paper, we settle this question. We show that M-Res has an exponential advantage over not only LD-Q-Res, but even over LQU^+-Res and IRM, the most powerful among currently known resolution-based QBF proof systems. Combining this with results from Beyersdorff et al. 2020, we conclude that M-Res is incomparable with LQU-Res and LQU^+-Res. Our proof method reveals two additional and curious features about M-Res: (i) MRes is not closed under restrictions, and is hence not a natural proof system, and (ii) weakening axiom clauses with existential variables provably yields an exponential advantage over M-Res without weakening. We further show that in the context of regular derivations, weakening axiom clauses with universal variables provably yields an exponential advantage over M-Res without weakening. These results suggest that MRes is better used with weakening, though whether M-Res with weakening is closed under restrictions remains open. We note that even with weakening, M-Res continues to be simulated by eFrege + ∀red (the simulation of ordinary M-Res was shown recently by Chew and Slivovsky).

READ FULL TEXT

page 1

page 3

page 11

page 17

page 18

research
07/20/2021

QRAT Polynomially Simulates Merge Resolution

Merge Resolution (MRes [Beyersdorff et al. J. Autom. Reason.'2021] ) is ...
research
04/24/2023

How can we prove that a proof search method is not an instance of another?

We introduce a method to prove that a proof search method is not an inst...
research
12/12/2020

Hard QBFs for Merge Resolution

We prove the first proof size lower bounds for the proof system Merge Re...
research
12/21/2021

Extending Merge Resolution to a Family of Proof Systems

Merge Resolution (MRes [Beyersdorff et al. J. Autom. Reason.'2021]) is a...
research
10/13/2022

Towards Uniform Certification in QBF

We pioneer a new technique that allows us to prove a multitude of previo...
research
02/11/2022

Notes on switching lemmas

We prove three switching lemmas, for random restrictions for which varia...
research
06/02/2022

Revisiting the General Identifiability Problem

We revisit the problem of general identifiability originally introduced ...

Please sign up or login with your details

Forgot password? Click here to reset