Efficient controller synthesis for consumption games with multiple resource types

  • Authors:

  • Tomáš Brázdil;Krishnendu Chatterjee;Antonín Kučera;Petr Novotný

  • Affiliations:

  • Faculty of Informatics, Masaryk University, Brno, Czech Republic;IST Austria, Klosterneuburg, Austria;Faculty of Informatics, Masaryk University, Brno, Czech Republic;Faculty of Informatics, Masaryk University, Brno, Czech Republic

  • Venue:
  • CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
  • Year:
  • 2012

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Abstract

We introduce consumption games, a model for discrete interactive system with multiple resources that are consumed or reloaded independently. More precisely, a consumption game is a finite-state graph where each transition is labeled by a vector of resource updates, where every update is a non-positive number or ω. The ω updates model the reloading of a given resource. Each vertex belongs either to player □ or player ◇, where the aim of player □ is to play so that the resources are never exhausted. We consider several natural algorithmic problems about consumption games, and show that although these problems are computationally hard in general, they are solvable in polynomial time for every fixed number of resource types (i.e., the dimension of the update vectors) and bounded resource updates.