# Graph Neural Reasoning for 2-Quantified Boolean Formula Solvers

@article{Yang2019GraphNR, title={Graph Neural Reasoning for 2-Quantified Boolean Formula Solvers}, author={Zhanfu Yang and Fei Wang and Ziliang Chen and Guannan Wei and Tiark Rompf}, journal={ArXiv}, year={2019}, volume={abs/1904.12084} }

In this paper, we investigate the feasibility of learning GNN (Graph Neural Network) based solvers and GNN-based heuristics for specified QBF (Quantified Boolean Formula) problems. [... ] Key Method Then we show how to learn a heuristic CEGAR 2QBF solver. We further explore generalizing GNN-based heuristics to larger unseen instances, and uncover some interesting challenges. In summary, this paper provides a comprehensive surveying view of applying GNN-embeddings to specified QBF solvers, and aims to offer… Expand

## 8 Citations

Graph Neural Reasoning May Fail in Certifying Boolean Unsatisfiability

- Computer ScienceArXiv
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This work demonstrates how to learn efficient heuristics for automated reasoning algorithms for quantified Boolean formulas through deep reinforcement learning on a backtracking search algorithm that solves significantly more formulas compared to the existing handwritten heuristic.

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A Bidirectional Graph Reasoning Network (BGRNet), which incorporates graph structure into the conventional panoptic segmentation network to mine the intra-modular and inter- modular relations within and between foreground things and background stuff classes, and proposes a Biddirectional Graph Connection Module to diffuse information across branches in a learnable fashion.

## References

SHOWING 1-10 OF 17 REFERENCES

Abstraction-Based Algorithm for 2QBF

- Computer ScienceSAT
- 2011

This paper proposes an algorithm for solving 2QBF satisfiability by counterexample guided abstraction refinement (CEGAR) and presents a comparison of a prototype implementing the presented algorithm to state of the art QBF solvers, showing that a larger set of instances is solved.

Towards Generalization in QBF Solving via Machine Learning

- Computer ScienceAAAI
- 2018

This paper argues that a solver benefits from generalizing a set of individual wins into a strategy on top of the competitive RAReQS algorithm by utilizing machine learning, which enables learning shorter strategies.

Solving QBF with counterexample guided refinement

- Computer ScienceArtif. Intell.
- 2016

Two promising avenues in QBF are opened: CEGAR-driven solvers as an alternative to existing approaches and a novel type of learning in DPLL.

Computing Vertex Eccentricity in Exponentially Large Graphs: QBF Formulation and Solution

- Computer ScienceSAT
- 2003

This work proposes a novel SAT-based decision procedure optimized for Quantified Boolean Formulas (QBFs) and presents encouraging experimental evidence showing its superiority to other public-domain solvers.

A Model for Generating Random Quantified Boolean Formulas

- Computer ScienceIJCAI
- 2005

This work defines and study a general model for generating random QBF instances, and exhibits experimental results showing that the model bears certain desirable similarities to the random SAT model, as well as a number of theoretical results concerning the model.

An Effective Algorithm for the Futile Questioning Problem

- Computer ScienceJournal of Automated Reasoning
- 2005

This paper develops a solution algorithm for the general case of Q-ALL SAT that uses a backtracking search and a new form of learning of clauses and is substantially faster than state-of-the-art solvers for quantified Boolean formulas.

Incremental Determinization

- Computer ScienceSAT
- 2016

A novel approach to solve quantified boolean formulas with one quantifier alternation (2QBF) in analogy to search algorithms for SAT and explains how propagation, decisions, and conflicts are lifted from values to Skolem functions.

Understanding and Extending Incremental Determinization for 2QBF

- Computer ScienceCAV
- 2018

This paper formalizes incremental determinization as a set of inference rules to help understand the design space of similar algorithms and presents additional inference rules that extend incremental determination in two ways.

Learning To Solve Circuit-SAT: An Unsupervised Differentiable Approach

- Computer ScienceICLR
- 2019

A neural framework that can learn to solve the Circuit Satisfiability problem by building upon a rich embedding architecture that encodes the problem structure and an end-to-end differentiable training procedure that mimics Reinforcement Learning and trains the model directly toward solving the SAT problem.

The complexity of theorem-proving procedures

- Mathematics, Computer ScienceSTOC
- 1971

It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a…