Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

Parity Games

  • Tim A. C. WillemseEmail author
  • Maciej Gazda
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_591

Years and Authors of Summarized Original Work

  • 1991; Emerson, Jutla

  • 1991; Mostowski

Problem Definition

A parity game is an infinite duration game, played by players odd and even, denoted by \(\square \)


Automata Computer-aided verification Determinacy Infinite duration games Perfect information Two-player games 
This is a preview of subscription content, log in to check access.

Recommended Reading

  1. 1.
    Emerson E, Jutla C (1991) Tree automata, mu-calculus and determinacy. In: FOCS’91. IEEE Computer Society, Washington, DC, pp 368–377. 10.1109/SFCS.1991.185392Google Scholar
  2. 2.
    Emerson E, Jutla C, Sistla A (2001) On model checking for the μ-calculus and its fragments. Theor Comput Sci 258(1–2):491–522. 10.1016/S0304-3975(00)00034-7MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Friedmann O (2011) An exponential lower bound for the latest deterministic strategy iteration algorithms. Log Methods Comput Sci 7(3)Google Scholar
  4. 4.
    Friedmann O (2013) A superpolynomial lower bound for strategy iteration based on snare memorization. Discret Appl Math 161(10–11):1317–1337MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Jurdziński M (1998) Deciding the winner in parity games is in UP \(\cap \) co-UP. IPL 68(3):119–124. 10.1016/S0020-0190(98)00150-1MathSciNetCrossRefGoogle Scholar
  6. 6.
    Jurdziński M (2000) Small progress measures for solving parity games. In: STACS’00. LNCS, vol 1770. Springer, pp 290–301. 10.1007/3-540-46541-3_24Google Scholar
  7. 7.
    Jurdziński M, Paterson M, Zwick U (2006) A deterministic subexponential algorithm for solving parity games. In: SODA’06. ACM/SIAM, pp 117–123. 10.1145/1109557.1109571Google Scholar
  8. 8.
    King V, Kupferman O, Vardi MY (2001) On the complexity of parity word automata. In: FOSSACS. LNCS, vol 2030. Springer, pp 276–286. 10.1007/3-540-45315-6_18Google Scholar
  9. 9.
    Martin D (1975) Borel determinacy. Ann Math 102:363–371. 10.2307/1971035MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    McNaughton R (1993) Infinite games played on finite graphs. APAL 65(2):149–184. 10.1016/0168-0072(93)90036-DMathSciNetzbMATHGoogle Scholar
  11. 11.
    Mostowski A (1991) Hierarchies of weak automata and weak monadic formulas. Theor Comput Sci 83(2):323–335. 10.1016/0304-3975(91)90283-8MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Niwinski D (1997) Fixed point characterization of infinite behavior of finite-state systems. Theor Comput Sci 189(1–2):1–69. 10.1016/S0304-3975(97)00039-XMathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Schewe S (2007) Solving parity games in big steps. In: FSTTCS’07. LNCS, vol 4855. Springer, pp 449–460. 10.1007/978-3-540-77050-3Google Scholar
  14. 14.
    Vöge J, Jurdzinski M (2000) A discrete strategy improvement algorithm for solving parity games. In: Emerson EA, Sistla AP (eds) CAV. LNCS, vol 1855. Springer, Heidelberg, pp 202–215Google Scholar
  15. 15.
    Zielonka W (1998) Infinite games on finitely coloured graphs with applications to automata on infinite trees. TCS 200(1–2):135–183. 10.1016/S0304-3975(98)00009-7MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mathematics and Computer Science, Eindhoven University of TechnologyEindhovenThe Netherlands