City Research Online

The Big-O Problem for Max-Plus Automata is Decidable (PSPACE-Complete)

Daviaud, L. ORCID: 0000-0002-9220-7118 & Purser, D. (2023). The Big-O Problem for Max-Plus Automata is Decidable (PSPACE-Complete). In: 2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). LICS 2023, 26-29 June 2023, Boston, USA. doi: 10.1109/LICS56636.2023.10175798


We show that the big-O problem for max-plus automata, i.e. weighted automata over the semiring (N ∪ {−∞}, max, +), is decidable and PSPACE-complete. The big-O (or affine domination) problem asks whether, given two max-plus automata computing functions f and g, there exists a constant c such that f ≤ cg + c. This is a relaxation of the containment problem asking whether f ≤ g, which is undecidable. Our decidability result uses Simon’s forest factorisation theorem, and relies on detecting specific elements, that we call witnesses, in a finite semigroup closed under two special operations: stabilisation and flattening.

Publication Type: Conference or Workshop Item (Paper)
Additional Information: © 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments: School of Science & Technology > Computer Science
[thumbnail of lics.pdf]
Text - Accepted Version
Download (495kB) | Preview


Add to AnyAdd to TwitterAdd to FacebookAdd to LinkedinAdd to PinterestAdd to Email


Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login