Proof Complexity of Symbolic QBF Reasoning

04/06/2021
by   Stefan Mengel, et al.
0

We introduce and investigate symbolic proof systems for Quantified Boolean Formulas (QBF) operating on Ordered Binary Decision Diagrams (OBDDs). These systems capture QBF solvers that perform symbolic quantifier elimination, and as such admit short proofs of formulas of bounded path-width and quantifier complexity. As a consequence, we obtain exponential separations from standard clausal proof systems, specifically (long-distance) QU-Resolution and IR-Calc. We further develop a lower bound technique for symbolic QBF proof systems based on strategy extraction that lifts known lower bounds from communication complexity. This allows us to derive strong lower bounds against symbolic QBF proof systems that are independent of the variable ordering of the underlying OBDDs, and that hold even if the proof system is allowed access to an NP-oracle.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/12/2020

Hard QBFs for Merge Resolution

We prove the first proof size lower bounds for the proof system Merge Re...
research
12/11/2017

Size, Cost, and Capacity: A Semantic Technique for Hard Random QBFs

As a natural extension of the SAT problem, an array of proof systems for...
research
12/02/2019

Exponential Resolution Lower Bounds for Weak Pigeonhole Principle and Perfect Matching Formulas over Sparse Graphs

We show exponential lower bounds on resolution proof length for pigeonho...
research
05/23/2020

MaxSAT Resolution and Subcube Sums

We study the MaxRes rule in the context of certifying unsatisfiability. ...
research
06/17/2023

Notes on "Bounds on BDD-Based Bucket Elimination”

This paper concerns Boolean satisfiability (SAT) solvers based on Ordere...
research
06/30/2011

Towards Understanding and Harnessing the Potential of Clause Learning

Efficient implementations of DPLL with the addition of clause learning a...
research
09/10/2021

Understanding the Relative Strength of QBF CDCL Solvers and QBF Resolution

QBF solvers implementing the QCDCL paradigm are powerful algorithms that...

Please sign up or login with your details

Forgot password? Click here to reset