Abstract
We present a new complementation construction for nondeterministic automata on finite trees. The traditional complementation involves determinization of the corresponding bottom-up automaton (recall that top-down deterministic automata are less powerful than nondeterministic automata, whereas bottom-up deterministic automata are equally powerful).The construction works directly in a top-down fashion, therefore without determinization. The main advantages of this construction are: (i) in the special case of finite words it boils down to the standard subset construction (which is not the case of the traditional bottom-up complementation construction), and (ii) it illustrates the core argument of the complementation lemma for infinite trees, central in the proof of Rabin's tree theorem, in a simpler setting where issues related to acceptance conditions over infinite words and determinacy of infinite games are not present.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.