Randomness for free Journal Article


Author(s): Chatterjee, Krishnendu; Doyen, Laurent; Gimbert, Hugo; Henzinger, Thomas A
Article Title: Randomness for free
Affiliation IST Austria
Abstract: We consider two-player zero-sum games on graphs. These games can be classified on the basis of the information of the players and on the mode of interaction between them. On the basis of information the classification is as follows: (a) partial-observation (both players have partial view of the game); (b) one-sided complete-observation (one player has complete observation); and (c) complete-observation (both players have complete view of the game). On the basis of mode of interaction we have the following classification: (a) concurrent (both players interact simultaneously); and (b) turn-based (both players interact in turn). The two sources of randomness in these games are randomness in transition function and randomness in strategies. In general, randomized strategies are more powerful than deterministic strategies, and randomness in transitions gives more general classes of games. In this work we present a complete characterization for the classes of games where randomness is not helpful in: (a) the transition function probabilistic transition can be simulated by deterministic transition); and (b) strategies (pure strategies are as powerful as randomized strategies). As consequence of our characterization we obtain new undecidability results for these games.
Keywords: Transition functions; General class; Partial views; Undecidability; Finite state; Partial observation; Randomized strategy; Zero-sum game
Journal Title: Information and Computation
Volume: 245
ISSN: 0890-5401
Publisher: Elsevier  
Date Published: 2015-12-01
Start Page: 3
End Page: 16
URL:
DOI: 10.1016/j.ic.2015.06.003
Notes: This research was partly supported by Austrian Science Fund (FWF) Grant No P 23499- N23, FWF NFN Grant No S11407-N23 and S11402-N23 (RiSE), ERC Start grant (279307: Graph Games), Microsoft faculty fellows award, the ERC Advanced Grant QUAREM (267989: Quantitative Reactive Modeling), European project Cassting (FP7-601148), European project COMBEST215543, and the European Network of Excellence ArtistDesign214373.
Open access: yes (repository)
IST Austria Authors
  1. Thomas A. Henzinger
    415 Henzinger
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