Degrees of Ambiguity of Büchi Tree Automata

Authors Alexander Rabinovich , Doron Tiferet

Thumbnail PDF


  • Filesize: 0.5 MB
  • 14 pages

Document Identifiers

Author Details

Alexander Rabinovich
  • Tel Aviv University, Israel
Doron Tiferet
  • Tel Aviv University, Israel

Cite AsGet BibTex

Alexander Rabinovich and Doron Tiferet. Degrees of Ambiguity of Büchi Tree Automata. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 50:1-50:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


An automaton is unambiguous if for every input it has at most one accepting computation. An automaton is finitely (respectively, countably) ambiguous if for every input it has at most finitely (respectively, countably) many accepting computations. An automaton is boundedly ambiguous if there is k in N, such that for every input it has at most k accepting computations. We consider nondeterministic Büchi automata (NBA) over infinite trees and prove that it is decidable in polynomial time, whether an automaton is unambiguous, boundedly ambiguous, finitely ambiguous, or countably ambiguous.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automata over infinite objects
  • automata on infinite trees
  • ambiguous automata


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. André Arnold. Rational omega-Languages are Non-Ambiguous. Theor. Comput. Sci., 26:221-223, September 1983. URL:
  2. Vince Bárány, Łukasz Kaiser, and Alex Rabinovich. Expressing cardinality quantifiers in monadic second-order logic over trees. Fundamenta Informaticae, 100(1-4):1-17, 2010. Google Scholar
  3. Arnaud Carayol, Christof Löding, Damian Niwinski, and Igor Walukiewicz. Choice functions and well-orderings over the infinite binary tree. Open Mathematics, 8(4):662-682, 2010. Google Scholar
  4. Thomas Colcombet. Unambiguity in automata theory. In International Workshop on Descriptional Complexity of Formal Systems, pages 3-18. Springer, 2015. Google Scholar
  5. Yo-Sub Han, Arto Salomaa, and Kai Salomaa. Ambiguity, nondeterminism and state complexity of finite automata. Acta Cybernetica, 23(1):141-157, 2017. Google Scholar
  6. Ernst Leiss. Succinct representation of regular languages by Boolean automata. Theoretical computer science, 13(3):323-330, 1981. Google Scholar
  7. Hing Leung. Descriptional complexity of NFA of different ambiguity. International Journal of Foundations of Computer Science, 16(05):975-984, 2005. Google Scholar
  8. Christof Löding and Anton Pirogov. On Finitely Ambiguous Büchi Automata. In Developments in Language Theory - 22nd International Conference, DLT 2018, Tokyo, Japan, September 10-14, 2018, Proceedings, pages 503-515, 2018. URL:
  9. Dominique Perrin and Jean-Éric Pin. Infinite words: automata, semigroups, logic and games, volume 141. Academic Press, 2004. Google Scholar
  10. Alexander Rabinovich. Complementation of Finitely Ambiguous Büchi Automata. In International Conference on Developments in Language Theory, pages 541-552. Springer, 2018. Google Scholar
  11. Alexander Rabinovich and Doron Tiferet. Degree of Ambiguity for Tree Automata and Tree Languages, forthcoming. Google Scholar
  12. Helmut Seidl. On the finite degree of ambiguity of finite tree automata. Acta Informatica, 26(6):527-542, 1989. Google Scholar
  13. Wolfgang Thomas. Automata on infinite objects. In Formal Models and Semantics, pages 133-191. Elsevier, 1990. Google Scholar
  14. Andreas Weber and Helmut Seidl. On the degree of ambiguity of finite automata. Theoretical Computer Science, 88(2):325-349, 1991. Google Scholar