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Invariant Projections in Games

13 pagesPublished: September 29, 2016


Identification of implicit structures in dynamic systems is a fundamental problem in Artificial Intelligence. In this paper, we focus on General Game Playing where games are modeled as finite state machines. We define a new property of game states called invariant projections which strongly corresponds to humans' intuition of game boards and may be applied in General Game Playing to support powerful heuristics, and to automate the design of game visualizations. We prove that the computation of invariant projections is Pi_{2}^{P}-complete in the size of the game description. We also show that invariant projections form a lattice, and the lattice ordering may be used to reduce the time to compute invariant projections potentially by a factor that is exponential in the schema size of game states. To enable competitive general game players to efficiently identify boards, we propose a sound (but incomplete) heuristic for computing invariant projections and evaluate its performance.

Keyphrases: dynamic systems, Game Description Language, game structures, General Game Playing, invariant projections

In: Christoph Benzmüller, Geoff Sutcliffe and Raul Rojas (editors). GCAI 2016. 2nd Global Conference on Artificial Intelligence, vol 41, pages 227--239

BibTeX entry
  author    = {Abhijeet Mohapatra and Bertrand Decoster and Sudhir Agarwal and Michael Genesereth},
  title     = {Invariant Projections in Games},
  booktitle = {GCAI 2016. 2nd Global Conference on Artificial Intelligence},
  editor    = {Christoph Benzm\textbackslash{}"uller and Geoff Sutcliffe and Raul Rojas},
  series    = {EPiC Series in Computing},
  volume    = {41},
  pages     = {227--239},
  year      = {2016},
  publisher = {EasyChair},
  bibsource = {EasyChair,},
  issn      = {2398-7340},
  url       = {},
  doi       = {10.29007/z5zn}}
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