eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-08-21
40:1
40:15
10.4230/LIPIcs.MFCS.2023.40
article
Universality and Forall-Exactness of Cost Register Automata with Few Registers
Daviaud, Laure
1
https://orcid.org/0000-0002-9220-7118
Ryzhikov, Andrew
2
https://orcid.org/0000-0002-2031-2488
School of Computing Sciences, University of East Anglia, Norwich, UK
Department of Computer Science, University of Oxford, UK
The universality problem asks whether a given finite state automaton accepts all the input words. For quantitative models of automata, where input words are mapped to real values, this is naturally extended to ask whether all the words are mapped to values above (or below) a given threshold. This is known to be undecidable for commonly studied examples such as weighted automata over the positive rational (plus-times) or the integer tropical (min-plus) semirings, or equivalently cost register automata (CRAs) over these semirings. In this paper, we prove that when restricted to CRAs with only three registers, the universality problem is still undecidable, even with additional restrictions for the CRAs to be copyless linear with resets.
In contrast, we show that, assuming the unary encoding of updates, the ∀-exact problem (does the CRA output zero on all the words?) for integer min-plus linear CRAs can be decided in polynomial time if the number of registers is constant. Without the restriction on the number of registers this problem is known to be PSPACE-complete.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol272-mfcs2023/LIPIcs.MFCS.2023.40/LIPIcs.MFCS.2023.40.pdf
cost register automata
universality
forall-exact problem
decidability