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

Daviaud, Laure and Purser, David (2023) The Big-O Problem for Max-Plus Automata is Decidable (PSPACE-Complete). In: 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). Proceedings - Symposium on Logic in Computer Science . The Institute of Electrical and Electronics Engineers (IEEE). ISBN 9798350335873

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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: Book Section
Additional Information: Funding Information: The first author has been supported for this work by the EPSRC grant EP/T018313/1. The second author was partially supported by the ERC grant INFSYS, agreement no. 950398.
Uncontrolled Keywords: software,mathematics(all),4* ,/dk/atira/pure/subjectarea/asjc/1700/1712
Faculty \ School: Faculty of Science > School of Computing Sciences
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Depositing User: LivePure Connector
Date Deposited: 14 Jun 2023 14:26
Last Modified: 31 Oct 2023 02:48
DOI: 10.1109/LICS56636.2023.10175798

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