Integer Weighted Automata on Infinite Words
: Halava Vesa, Harju Tero, Niskanen Reino, Potapov Igor
Publisher: WORLD 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
DOI: https://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.