Journal of Computer Science and Technology

, Volume 28, Issue 2, pp 278–284 | Cite as

On the Toggling-Branching Recurrence of Computability Logic

  • Mei-Xia Qu
  • Jun-Feng Luan
  • Da-Ming Zhu
  • Meng Du
Regular Paper


We introduce a new, substantially simplified version of the toggling-branching recurrence operation of computability logic, prove its equivalence to Japaridze’s old, “canonical” version, and also prove that both versions preserve the static property of their arguments.


computability logic game semantics interactive computation static game 


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Supplementary material

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  1. [1]
    Japaridze G (2003) Introduction to computability logic. Annals of Pure and Applied Logic 123(1/3):1–99MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    Bauer M S. A PSPACE-complete first order fragment of computability logic., Jan. 2012.
  3. [3]
    Japaridze G. Computability logic: A formal theory of interaction. In Interactive Computation: The New Paradigm, Goldin D, Smolka S A, Wegner P (eds.), Springer, 2006, pp.183–223.Google Scholar
  4. [4]
    Japaridze G. In the beginning was game semantics. In Games: Unifying Logic, Language, and Philosophy, Majer O, Pietarinen A V, Tulenheimo T (eds.), Springer, 2009, pp.249–350.Google Scholar
  5. [5]
    Japaridze G (2009) Many concepts and two logics of algorithmic reduction. Studia Logica 91(1):1–24MathSciNetzbMATHCrossRefGoogle Scholar
  6. [6]
    Japaridze G (2011) Toggling operators in computability logic. Theoretical Computer Science 412(11):971–1004MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    Japaridze G (2012) A new face of the branching recurrence of computability logic. Applied Mathematics Letters 25(11):1585–1589MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    Japaridze G (2013) The taming of recurrences in computability logic through cirquent calculus, Part I. Archive for Mathematical Logic 52(1/2):173–212MathSciNetzbMATHCrossRefGoogle Scholar
  9. [9]
    Japaridze G (2013) The taming of recurrences in computability logic through cirquent calculus, Part II. Archive for Mathematical Logic 52(1/2):213–259MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    Kwon K, Hur S (2010) Adding sequential conjunctions to Prolog. J Compu Tech and Applicat 1(1):1–3Google Scholar
  11. [11]
    Mezhirov I, Vereshchagin N (2010) On abstract resource semantics and computability logic. Journal of Computer and System Sciences 76(5):356–372MathSciNetzbMATHCrossRefGoogle Scholar
  12. [12]
    Xu WY, Liu SY (2012) The countable versus uncountable branching recurrences in computability logic. Journal of Applied Logic 10(4):431–446MathSciNetCrossRefGoogle Scholar
  13. [13]
    Xu WY, Liu SY (2013) The parallel versus branching recurrences in computability logic. Notre Dame Journal of Formal Logic 54(1):61–78zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York & Science Press, China 2013

Authors and Affiliations

  • Mei-Xia Qu
    • 1
    • 2
  • Jun-Feng Luan
    • 1
  • Da-Ming Zhu
    • 1
  • Meng Du
    • 2
  1. 1.School of Computer Science and TechnologyShandong UniversityJinanChina
  2. 2.School of Mechanical, Electrical and Information EngineeringShandong University at WeihaiWeihaiChina

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