On the synthesis of a reactive module
POPL '89 Proceedings of the 16th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Reasoning about infinite computations
Information and Computation
Relating Hierarchies of Word and Tree Automata
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Automata logics, and infinite games: a guide to current research
Automata logics, and infinite games: a guide to current research
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
On the complexity of omega -automata
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
The Theory of Stabilisation Monoids and Regular Cost Functions
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Finite automata and their decision problems
IBM Journal of Research and Development
Solving games without determinization
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
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Choices made by nondeterministic word automata depend on both the past (the prefix of the word read so far) and the future (the suffix yet to be read). In several applications, most notably synthesis, the future is diverse or unknown, leading to algorithms that are based on deterministic automata. Hoping to retain some of the advantages of nondeterministic automata, researchers have studied restricted classes of nondeterministic automata. Three such classes are nondeterministic automata that are good for trees (GFT; i.e., ones that can be expanded to tree automata accepting the derived tree languages, thus whose choices should satisfy diverse futures), good for games (GFG; i.e., ones whose choices depend only on the past), and determinizable by pruning (DBP; i.e., ones that embody equivalent deterministic automata). The theoretical properties and relative merits of the different classes are still open, having vagueness on whether they really differ from deterministic automata. In particular, while DBP ⊆ GFG ⊆ GFT, it is not known whether every GFT automaton is GFG and whether every GFG automaton is DBP. Also open is the possible succinctness of GFG and GFT automata compared to deterministic automata. We study these problems for ω-regular automata with all common acceptance conditions. We show that GFT=GFG⊃DBP, and describe a determinization construction for GFG automata.