About the effect of the number of successful paths in an infinite tree on the recognizability by a finite automaton with Buchi conditions
We modify an acceptance condition of Büchi automaton on infinite trees: rather than to require that each computation path is successful, we impose various restrictions on the number of successful paths in a run of the automaton on a tree. All these modifications alter the recognizing power of Büchi automata. We examine the classes induced by the acceptance conditions that require ≤α, ≥α, =α successful paths, where α is a cardinal number. It turns out that, except some trivial cases, the “≤” classes are uncomparable with the class Bü of Büchi acceptable tree languages, while the classes “≥” are strictly included in Bü.
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- Büchi,J.R. (1962) On a decision method in restricted second order arithmetic, in “Logic, Methodology and Philosophy of Science. Proc.1960 Intern. Congr. (E.Nagel et al. eds.),pp. 1–11.Google Scholar
- Emerson, E.A. and Jutla, C. (1988) The Complexity of Tree Automata and Logics of Programs, Proc. 29th IEEE FOCS,pp. 328–337.Google Scholar
- Rabin, M.O. (1969) Decidability of second-order theories and automata on infinite trees, Trans. AMS 141, pp. 1–35.Google Scholar
- Rabin, M.O. (1970) Weakly definable relations and special automata, in “Mathematical Logic and Foundations of Set Theory” (Y.Bar-Hillel, ed.), pp. 1–23.Google Scholar
- Street R.S. (1982), Propositional dynamic logic of looping and converse, Inform. Contr. 54, pp. 121–141.Google Scholar
- Thomas, W. (1990), Automata on Infinite Objects, in “Handbook of Theoretical Computer Science” (J.v.Leeuwen,ed.).Google Scholar
- Vardi, M.Y. and Stockmeyer, L. (1985), Improved Upper and Lower Bounds for Modal Logics of Programs, in Proc.26th FOCS.Google Scholar
- Vardi, M.Y. and Wolper, P. (1984), Automata-Theoretic Technics for Modal Logics of Programs in Proc. 16th ACM STOC, pp. 446–456.Google Scholar