---
title: "Abstract Cores in Implicit Hitting Set MaxSat Solving (Extended Abstract)"
authors:
  - "Jeremias Berg"
  - "Fahiem Bacchus"
  - "Alex Poole"
doi: "10.24963/ijcai.2021/643"
url: "https://ijcai.org/proceedings/2021/643"
pdf: "https://ijcai.org/proceedings/2021/0643.pdf"
venue: "Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence"
year: 2021
pages: "4745-4749"
track: "Sister Conferences Best Papers"
keywords:
  - "Constraints and SAT: Constraint Optimization"
  - "Constraints and SAT: SAT: Algorithms and Techniques"
  - "Constraints and SAT: Constraints: Modeling, Solvers, Applications"
  - "Constraints and SAT: MaxSAT, MinSAT"
---

# Abstract Cores in Implicit Hitting Set MaxSat Solving (Extended Abstract)

Jeremias Berg, Fahiem Bacchus, Alex Poole

*Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence*, pages 4745-4749. DOI: [10.24963/ijcai.2021/643](https://doi.org/10.24963/ijcai.2021/643)

## Abstract

Maximum satisfiability (MaxSat) solving  is an active area of research motivated by numerous successful applications to solving
NP-hard combinatorial optimization problems.  One of the most successful approaches for solving MaxSat instances from real world domains 
are the so called  implicit hitting set (IHS) solvers. IHS solvers decouple MaxSat solving into separate core-extraction (i.e. reasoning) and optimization steps which are tackled by a Boolean satisfiability (SAT)  and an integer linear programming (IP) solver, respectively. While the approach shows state-of-the-art performance on many industrial instances, 
it is known that there exists instances on which IHS solvers need to extract an exponential number of cores before terminating. Motivated by the simplest of these problematic instances, we propose abstract cores,  a compact representation for a potentially exponential number of regular cores. We demonstrate how to incorporate abstract core reasoning into the IHS algorithm and report on an empirical evaluation demonstrating, that including abstract cores into a state-of-the-art IHS solver improves its performance enough to surpass the best performing solvers of the 2019 MaxSat Evaluation.