Fixed-Point Characterisation of Winning Strategies in Impartial Games

  • Roland Backhouse
  • Diethard Michaelis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3051)


We use fixed-point calculus to characterise winning strategies in impartial, two-person games. A byproduct is the fixed-point characterisation of winning, losing and stalemate positions. We expect the results to be most useful in teaching calculational reasoning about least and greatest fixed points.


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  1. [BCG82]
    Berlekamp, E.R., Conway, J.H., Guy, R.K.: Winning Ways, vol. I&II. Academic Press, London (1982)zbMATHGoogle Scholar
  2. [DBvdW97]
    Doornbos, H., Backhouse, R., van der Woude, J.: A calculational approach to mathematical induction. Theoretical Computer Science 179(1-2), 103–135 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  3. [DS90]
    Dijkstra, E.W., Scholten, C.S.: Predicate Calculus and Program Semantics. Springer, Berlin (1990)zbMATHGoogle Scholar
  4. [SS93]
    Schmidt, G., Ströhlein, T.: Relations and Graphs, Discrete Mathematics for Computer Scientists. EATCS Monographs on Theoretical Computer Science. Springer, Berlin (1993)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Roland Backhouse
    • 1
  • Diethard Michaelis
    • 2
  1. 1.School of Computer Science and Information TechnologyUniversity of NottinghamNottinghamEngland
  2. 2. ZirndorfGermany

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