Year: 2026
Type: preprint
Abstract: We prove that deciding whether there is a surjective homomorphism from an arbitrary finitely presented inverse monoid onto the bicyclic monoid is $\mathsf{NP}$-complete. As part of the proof, we show that an extension of existential Presburger arithmetic which involves greatest common divisors on $n$ arguments is in $\mathsf{NP}$, extending a recent result of Défossez, Haase, Mansutti, and Pérez (SODA 2024).
Source: arXiv (Cornell University)
Authors: Carroll, Luka, Elder, Murray
Institution: University of Technology Sydney
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220993078