Abstract
AbstractWe 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.
Highlights
Markov chains are a very important modeling formalism in many areas of science
We showed that p-automata provide an automata-theoretic framework for reasoning about pCTL model checking, and abstraction of discrete time Markov chains
These are the obligations that have value 1, i.e., where the obligation of Player 0 is met. This gives rise to a simpler definition where we contrast a strategy of one player with the strategy of the other player as customary in definition of games. We show that this simpler definition, which does not work for the general case, coincides with the definition arising from the Martin-like reduction for Markov chains and finite turn-based stochastic parity games with obligations
Summary
Markov chains are a very important modeling formalism in many areas of science. In computer science, Markov chains form the basis of central techniques such as performance modeling, and the design and correctness of randomized algorithms used in security and communication protocols. We consider Markov chains with Borel objectives and obligations and finite turn-based stochastic parity games with obligations. We show that in these cases, we can embed the notion of winning into the structure of the game by using choice sets These are the obligations that have value 1, i.e., where the obligation of Player 0 is met. This gives rise to a simpler definition where we contrast a strategy of one player with the strategy of the other player as customary in definition of games We show that this simpler definition, which does not work for the general case, coincides with the definition arising from the Martin-like reduction for Markov chains and finite turn-based stochastic parity games with obligations. Our framework for turn-based stochastic obligation parity games could provide better algorithmic analysis for fragments of probabilistic μ-calculus of [22, 21]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
