Some properties of Higman-Thompson monoids and digital circuits
<|reference_start|>Some properties of Higman-Thompson monoids and digital circuits: We define various monoid versions of the R. Thompson group $V$, and prove connections with monoids of acyclic digital circuits. We show that the monoid $M_{2,1}$ (based on partial functions) is not embeddable into Thompson's monoid ${\sf tot}M_{2,1}$, but that ${\sf tot}M_{2,1}$ has a submonoid that maps homomorphically onto $M_{2,1}$. This leads to an efficient completion algorithm for partial functions and partial circuits. We show that the union of partial circuits with disjoint domains is an element of $M_{2,1}$, and conversely, every element of $M_{2,1}$ can be decomposed efficiently into a union of partial circuits with disjoint domains.<|reference_end|>
@article{birget2024some,
    title={Some properties of Higman-Thompson monoids and digital circuits},
    author={J.C. Birget},
    journal={arXiv preprint arXiv:2403.12674},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.12674},
    primaryClass={math.GR cs.CC}
}