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



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.

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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