Integer Weighted Automata on Infinite Words




Halava Vesa, Harju Tero, Niskanen Reino, Potapov Igor

PublisherWORLD SCIENTIFIC PUBL CO PTE LTD

2023

International Journal of Foundations of Computer Science

INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE

INT J FOUND COMPUT S

20

0129-0541

1793-6373

DOIhttps://doi.org/10.1142/S0129054122440014(external)

https://www.worldscientific.com/doi/10.1142/S0129054122440014(external)

https://researchonline.ljmu.ac.uk/id/eprint/17943/1/HHNP_author_copy.pdf(external)



In this paper we combine two classical generalisations of finite automata (weighted automata and automata on infinite words) into a model of integer weighted automata on infinite words and study the universality and the emptiness problems under zero weight acceptance. We show that the universality problem is undecidable for three-state automata by a direct reduction from the infinite Post correspondence problem. We also consider other more general acceptance conditions as well as their complements with respect to the universality and the emptiness problems. Additionally, we build a universal integer weighted automaton with fixed transitions. This automaton has an additional integer input that allows it to simulate any semi-Thue system.



Last updated on 2024-26-11 at 12:07