A Myhill-Nerode theorem for automata with advice
Alex Kruckman (Berkeley University), Sasha Rubin (TU Vienna, IST, Austria), John Sheridan, Ben Zax
TL;DR
This paper extends the classical Myhill-Nerode theorem to characterize the languages recognized by automata with advice, including finite string and tree automata, providing a theoretical foundation for automata with auxiliary information.
Contribution
It refines the Myhill-Nerode theorem to apply to automata with advice, offering a new characterization for both finite string and tree automata with advice.
Findings
Provides a characterization of languages accepted by automata with advice
Extends the Myhill-Nerode theorem to tree automata with advice
Establishes a theoretical framework for automata with auxiliary advice tapes
Abstract
An automaton with advice is a finite state automaton which has access to an additional fixed infinite string called an advice tape. We refine the Myhill-Nerode theorem to characterize the languages of finite strings that are accepted by automata with advice. We do the same for tree automata with advice.
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