This is a program for analysing Quantum Hackenbush, which is a quantum-inspired variant of the combinatorial game Hackenbush. The program takes as an input a description of a Hackenbush position, and computes a property such as the birthday, outcome class, or value, in the case where superposed moves are allowed. Unsuperposed moves may also be allowed, with the quantum-inspired "flavour" defining exactly when they are allowed.
This program was written by me (Jelle Pleunes) for a thesis named "Quantum-inspired Hackenbush", as part of the Computer Science master's programme at the Leiden Institute of Advanced Computer Science (LIACS), Leiden University. This thesis can be downloaded from the LIACS Thesis Repository. The slides for my final thesis presentation can be found here.
An in-depth analysis of Hackenbush (and combinatorial games in general) can be found in the following paper by E. R. Berlekamp, J. H. Conway, and R. K. Guy:
E. R. Berlekamp, J. H. Conway, and R. K. Guy. “Winning ways for your mathematical plays, Volume 1”. In: (No Title) (2001).
Quantum-inspired combinatorial games, with their different flavours, are defined in the paper by P. Dorbec and M. Mhalla:
P. Dorbec and M. Mhalla. “Toward quantum combinatorial games”. In: arXiv
preprint arXiv:1701.02193 (2017). URL: https://arxiv.org/abs/1701.02193.
This program was heavily inspired by CGSynch, which is a program for analysing combinatorial and synchronised games.
CGSynch was written for a bachelor thesis by X. Lenstra:
X. Lenstra. "A program for analysing combinatorial and synchronized games".
Bachelor thesis. LIACS, Leiden University, 2022. URL: https://theses.liacs.nl/2358.
This program was written for a master thesis by J. Pleunes:
J. Pleunes. "Quantum-inpired Hackenbush".
Master thesis. LIACS, Leiden University, 2024. URL: https://theses.liacs.nl/3110.