Daviaud, Laure and Purser, David ORCID: 0000-0003-0394-1634
(2023)
The Big-O Problem for Max-Plus Automata is Decidable (PSPACE-Complete).
In: Thirty-Eighth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 2023-6-26 - 2023-6-29, Boston, USA.
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Abstract
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.
Item Type: | Conference or Workshop Item (Unspecified) |
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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.” |
Uncontrolled Keywords: | 46 Information and Computing Sciences, 4904 Pure Mathematics, 49 Mathematical Sciences |
Divisions: | Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science |
Depositing User: | Symplectic Admin |
Date Deposited: | 18 Apr 2023 09:33 |
Last Modified: | 08 Nov 2024 15:20 |
DOI: | 10.1109/LICS56636.2023.10175798 |
Related URLs: | |
URI: | https://livrepository.liverpool.ac.uk/id/eprint/3169653 |