Acknowledgments

We thank Alexey Ignatiev and Joao Marques-Silva for their participation in related MaxSAT research discussions, and Elena Barrachina for reviewing parts of the Hermax documentation.

Solver References

Hermax builds on, integrates with, or is influenced by a broader SAT/MaxSAT and optimization ecosystem. Relevant references include:

SAT Solvers

Selected SAT solver references used across the wider ecosystem include Glucose [1], CaDiCaL [2], MiniSat [3], and CominiSatPS [4].

[1]

Gilles Audemard and Laurent Simon. On the glucose SAT solver. International Journal on Artificial Intelligence Tools, 27(01):1840001, 2018.

[2]

Armin Biere, Tobias Faller, Katalin Fazekas, Mathias Fleury, Nils Froleyks, and Florian Pollitt. CaDiCaL 2.0. International Conference on Computer Aided Verification, pages 133-152, 2024.

[3]

Niklas Sorensson and Niklas Een. Minisat v1.13 - a SAT solver with conflict-clause minimization. SAT, 53:1-2, 2005.

[4]

Chanseok Oh. COMiniSatPS Pulsar and GHackCOMSPS. In Tomas Balyo, Marijn J. H. Heule, and Matti Jarvisalo (eds.), Proceedings of SAT Competition 2017: Solver and Benchmark Descriptions, volume B-2017-1, pages 12-13, 2017. Department of Computer Science, University of Helsinki.

Python and SAT References

• Alexey Ignatiev, Antonio Morgado, Joao Marques-Silva. PySAT: A Python Toolkit for Prototyping with SAT Oracles. SAT 2018.

• Carlos Ansotegui, Jesus Ojeda, Antonio Pacheco, Josep Pon, Josep M. Salvia, Eduard Torres. Optilog: A framework for SAT-based systems. SAT 2021.

• Josep Alos, Carlos Ansotegui, Josep M. Salvia, Eduard Torres. Optilog V2: model, solve, tune and run. SAT 2022.

• Tias Guns. Increasing modeling language convenience with a universal n-dimensional array, CPpy as python-embedded example. Proceedings of the 18th workshop on Constraint Modelling and Reformulation at CP (ModRef 2019), volume 19, 2019.

• Nicholas Nethercote, Peter J. Stuckey, Ralph Becket, Sebastian Brand, Gregory J. Duck, Guido Tack. MiniZinc: Towards a standard CP modelling language. International Conference on Principles and Practice of Constraint Programming, pages 529-543, 2007.

• J. S. Roy, Stuart A. Mitchell, and PuLP contributors. PuLP, version 3.3.0, 2025. https://pypi.org/project/PuLP/

MaxSAT References

The following MaxSAT-focused academic references are currently cited across the Hermax documentation set:

• Andreas Niskanen, Jeremias Berg, Matti Järvisalo. Incremental Maximum Satisfiability. SAT 2022.

• Marek Piotrów. UWrMaxSat: Efficient Solver for MaxSAT and Pseudo-Boolean Problems. ICTAI 2020.

• Florent Avellaneda. EvalMaxSAT. MaxSAT Evaluation: Solver and Benchmark Descriptions, 2023.

• Alexey Ignatiev, Antonio Morgado, Joao Marques-Silva. RC2: An Efficient MaxSAT Solver. JSAT 11(1), 2019.

• Hannes Ihalainen, Jeremias Berg, Matti Järvisalo. Refined Core Relaxation for Core-Guided MaxSAT Solving. CP 2021.

• Jeremias Berg, Bart Bogaerts, Jakob Nordström, Andy Oertel, Dieter Vandesande. Certified Core-Guided MaxSAT Solving. CADE 29, 2023.

• Ruben Martins, Vasco Manquinho, Ines Lynce. Open-WBO: A Modular MaxSAT Solver. SAT 2014.

• Benjamin Andres, Benjamin Kaufmann, Oliver Matheis, Torsten Schaub. Unsatisfiability-based Optimization in clasp. ICLP 2012 Technical Communications.

• Saurabh Joshi, Prateek Kumar, Sukrut Rao, Ruben Martins. Open-WBO-Inc: Approximation Strategies for Incomplete Weighted MaxSAT. Journal on Satisfiability, Boolean Modelling and Computation 11(1), 2019.

• Shiwei Pan, Yiyuan Wang, Shaowei Cai. An Efficient Core-Guided Solver for Weighted Partial MaxSAT. IJCAI 2025.

• Mingming Jin, Kun He, Jiongzhi Zheng, Jinghui Xue, Zhuo Chen. Combining BandMaxSAT and FPS with SPB-MaxSAT-c. MaxSAT Evaluation 2024: Solver and Benchmark Descriptions, 2024.

• Menghua Jiang. NuWLS-c-IBR. MaxSAT Evaluation solver description, 2023.

• Jeremias Berg, Emir Demirovic, Peter J. Stuckey. Core-Boosted Linear Search for Incomplete MaxSAT. CPAIOR 2019.

• Xujie Si, Xin Zhang, Vasco Manquinho, Mikolás Janota, Alexey Ignatiev, Mayur Naik. On Incremental Core-Guided MaxSAT Solving. CP 2016.

• Alexey Ignatiev, Yacine Izza, Peter J. Stuckey, Joao Marques-Silva. Using MaxSAT for Efficient Explanations of Tree Ensembles. AAAI 2022.

• Tobias Paxian, Armin Biere. MaxSAT Fuzzing and Delta Debugging. Journal of Artificial Intelligence Research, 85, 2026.

• Andreas Niskanen, Jeremias Berg, Matti Järvisalo. Enabling Incrementality in the Implicit Hitting Set Approach to MaxSAT Under Changing Weights. CP 2021.

• Jessica Davies. Solving MaxSAT by Decoupling Optimization and Satisfaction. Doctoral dissertation, 2014.