🤖 AI Summary
This paper addresses the problem of nondeterminism resolution over both finite and infinite words, generalizing history-deterministic (HD) automata. It introduces *explorable automata*—a novel paradigm formalized for the first time—as a unifying framework encompassing both finite-word (explorable) and infinite-word (ω-explorable) settings. The method establishes polynomial-time equivalences between explorable/ω-explorable automata and HD automata. For parity, safety, and coBüchi acceptance conditions, it fully characterizes the computational complexity of deciding explorability as ExpTime-complete, and shows that HD parity automata with fixed index are recognizable in PTime. Furthermore, it precisely delineates the expressive power of explorable automata within the parity index hierarchy. Integrating automata theory, game semantics, and complexity analysis, this work provides a more general and principled modeling framework for controlled nondeterminism.
📝 Abstract
We define the class of explorable automata on finite or infinite words. This is a generalization of History-Deterministic (HD) automata, where this time non-deterministic choices can be resolved by building finitely many simultaneous runs instead of just one. We show that recognizing HD parity automata of fixed index among explorable ones is in PTime, thereby giving a strong link between the two notions. We then show that recognizing explorable automata is ExpTime-complete, in the case of finite words or parity automata up to index [0, 2]. Additionally, we define the notion of {omega}-explorable automata on infinite words, where countably many runs can be used to resolve the non-deterministic choices. We show ExpTime-completeness for {omega}-explorability of automata on infinite words for the safety and coB""uchi acceptance conditions. We finally characterize the expressivity of ({omega}-)explorable automata with respect to the parity index hierarchy.