Testing epimorphism onto the bicyclic monoid is $\mathsf{NP}$-complete

Luka Carroll; Murray Elder

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arXiv · 2610.08198

Testing epimorphism onto the bicyclic monoid is $\mathsf{NP}$-complete

Luka Carroll·Murray Elder

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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).

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Luka Carroll, Murray Elder. 2026-10-06. Testing epimorphism onto the bicyclic monoid is $\mathsf{NP}$-complete. https://arxiv.org/abs/2610.08198

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