GO Is Polynomial-Space Hard

  • Authors:
  • David Lichtenstein;Michael Sipser

  • Affiliations:
  • Computer Science Division, Department of Electrical Engineering and Computer Science, University of California, Berkeley, CA;IBM Research Laboratory, 5600 Cottle Road, San Jose, CA and University of California, Berkeley, California

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1980

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Abstract

It is shown that, given an arbitrary GO position on an n × n board, the problem of determining the winner is Pspace hard. New techniques are exploited to overcome the difficulties arising from the planar nature of board games. In particular, it is proved that GO is Pspace hard by reducing a Pspace-complete set, TQBF, to a game called generalized geography, then to a planar version of that game, and finally to GO.