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OBLIGATION BLACKWELL GAMES AND P-AUTOMATA

Published online by Cambridge University Press:  19 June 2017

KRISHNENDU CHATTERJEE  and
NIR PITERMAN
KRISHNENDU CHATTERJEE
Affiliation:
IST AUSTRIA KLOSTERNEUBURG AUSTRIA E-mail: krishnendu.chatterjee@ist.edu
NIR PITERMAN
Affiliation:
DEPARTMENT OF INFORMATICS UNIVERSITY OF LEICESTER LEICESTER, UK E-mail: nir.piterman@le.ac.uk
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Abstract

We generalize winning conditions in two-player games by adding a structural acceptance condition called obligations. Obligations are orthogonal to the linear winning conditions that define whether a play is winning. Obligations are a declaration that player 0 can achieve a certain value from a configuration. If the obligation is met, the value of that configuration for player 0 is 1.

We define the value in such games and show that obligation games are determined. For Markov chains with Borel objectives and obligations, and finite turn-based stochastic parity games with obligations we give an alternative and simpler characterization of the value function. Based on this simpler definition we show that the decision problem of winning finite turn-based stochastic parity games with obligations is in NP∩co-NP. We also show that obligation games provide a game framework for reasoning about p-automata.

Keywords

03B70automatatwo-player games

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Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 2 , June 2017 , pp. 420 - 452
Copyright
Copyright © The Association for Symbolic Logic 2017 

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