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Optimal Strategy Synthesis in Stochastic Müller Games [chapter]

Krishnendu Chatterjee
Foundations of Software Science and Computational Structures  
We present optimal memory bounds for pure almost-sure winning and optimal winning strategies in stochastic graph games with Müller winning conditions.  ...  In the case of stochastic reactive processes, the corresponding stochastic graph games have three players, two of them (System and Environment) behaving adversarially, and the third (Uncertainty) behaving  ...  in the synthesis problem.  ... 
doi:10.1007/978-3-540-71389-0_11 dblp:conf/fossacs/Chatterjee07 fatcat:x4gcexzul5atdo7b6pcd2hdmzm

Decision Problems for Nash Equilibria in Stochastic Games [chapter]

Michael Ummels, Dominik Wojtczak
2009 Lecture Notes in Computer Science  
We analyse the computational complexity of finding Nash equilibria in stochastic multiplayer games with ω-regular objectives.  ...  We also establish that the existence of a Nash equilibrium with a certain binary payoff entails the existence of an equilibrium with the same payoff in pure, finite-state strategies.  ...  Stochastic games with ω-regular objectives have been successfully applied in the verification and synthesis of reactive systems under the influence of random events.  ... 
doi:10.1007/978-3-642-04027-6_37 fatcat:ymug7i7nsfbkhm2ws6kicqmayi

Non-Zero Sum Games for Reactive Synthesis [article]

Romain Brenguier, Lorenzo Clemente, Paul Hunter, Guillermo A. Pérez, Mickael Randour, Jean-François Raskin, Ocan Sankur, Mathieu Sassolas
2015 arXiv   pre-print
In this invited contribution, we summarize new solution concepts useful for the synthesis of reactive systems that we have introduced in several recent publications.  ...  These solution concepts are developed in the context of non-zero sum games played on graphs. They are part of the contributions obtained in the inVEST project funded by the European Research Council.  ...  The above results are obtained by reducing the synthesis of regret-minimizing strategies to finding winning strategies in classical games.  ... 
arXiv:1512.05568v1 fatcat:i3kdtqwwtvcthgxpu5nx476ecy

Non-Zero Sum Games for Reactive Synthesis [chapter]

Romain Brenguier, Lorenzo Clemente, Paul Hunter, Guillermo A. Pérez, Mickael Randour, Jean-François Raskin, Ocan Sankur, Mathieu Sassolas
2016 Lecture Notes in Computer Science  
In this invited contribution, we summarize new solution concepts useful for the synthesis of reactive systems that we have introduced in several recent publications.  ...  These solution concepts are developed in the context of non-zero sum games played on graphs. They are part of the contributions obtained in the inVEST project funded by the European Research Council.  ...  The above results are obtained by reducing the synthesis of regret-minimizing strategies to finding winning strategies in classical games.  ... 
doi:10.1007/978-3-319-30000-9_1 fatcat:5p2o2ejvkfaung233lastkqux4

The complexity of stochastic Müller games

Krishnendu Chatterjee
2012 Information and Computation  
We present optimal memory bounds for pure (deterministic) almost-sure winning and optimal winning strategies in stochastic graph games with Müller winning conditions.  ...  Our results are relevant in synthesis of stochastic reactive processes.  ...  in the synthesis problem.  ... 
doi:10.1016/j.ic.2011.11.004 fatcat:y6sibd5a6fcphlrdrmtwub2qtm

A survey of stochastic ω-regular games

Krishnendu Chatterjee, Thomas A. Henzinger
2012 Journal of computer and system sciences (Print)  
We summarize classical and recent results about two-player games played on graphs with ω-regular objectives. These games have applications in the verification and synthesis of reactive systems.  ...  Important distinctions are whether a graph game is turn-based or concurrent; deterministic or stochastic; zero-sum or not.  ...  By contrast, in certain special cases-for example, in the case of turn-based stochastic games with parity objectives-optimal and winning strategies require neither randomization nor memory; such pure memoryless  ... 
doi:10.1016/j.jcss.2011.05.002 fatcat:267iudbahzf4tdef2fo573l3ie

The Complexity of Nash Equilibria in Stochastic Multiplayer Games

Michael Ummels, Dominik Wojtczak, Wolfgang Thomas
2011 Logical Methods in Computer Science  
We analyse the computational complexity of finding Nash equilibria in turn-based stochastic multiplayer games with omega-regular objectives.  ...  In particular, we prove that deciding the existence of an equilibrium in which each player either wins or loses with probability 1 can be done in polynomial time for games where the objective of each player  ...  τ i of the coalition Π \ {i} in the coalition game G i .  ... 
doi:10.2168/lmcs-7(3:20)2011 fatcat:i4ggd6mxyfcoljokr2s7y3mtgq

Solving Random Parity Games in Polynomial Time [article]

Richard Combes, Mikael Touati
2020 arXiv   pre-print
We further show that non-sparse games can be solved in time O(| V|) with high probability, and emit a conjecture concerning the hardness of the d=2 case.  ...  The design of SWCP is based on the threshold for the appearance of particular types of cycles in the players' respective subgraphs.  ...  As in all optimal control problems, in order to find the optimal strategy in the current state (i.e. the current location of the token), it is sufficient to know the optimal strategy for all successors  ... 
arXiv:2007.08387v1 fatcat:ybur6jrpvjfgrn4z3l6vphucj4

Computer aided synthesis: a game theoretic approach [article]

Véronique Bruyère
2017 arXiv   pre-print
In this invited contribution, we propose a comprehensive introduction to game theory applied in computer aided synthesis.  ...  In this context, we give some classical results on two-player zero-sum games and then on multi-player non zero-sum games.  ...  k the optimal strategy τ ρ k −i (in (G i , ρ k )).  ... 
arXiv:1706.00652v1 fatcat:rn732kpv35gtrpomg5pvw7jepa

Recent advances in interactive and automated analysis

Radu Mateescu
2017 International Journal on Software Tools for Technology Transfer (STTT)  
In this context, formal methods equipped with powerful and versatile analysis tools are more important than ever in the design process.  ...  Despite the relevant scientific results and well-established tools obtained in recent years, there is a constant need of enhancing the analysis capabilities in order to handle increasingly complex systems  ...  Another illustration of extending PRISM is described in the paper PRISM-games: Verification and Strategy Synthesis for Stochastic Multi-player Games with Multiple Objectives [29] by Marta Kwiatkowska  ... 
doi:10.1007/s10009-017-0477-y fatcat:ouhrg3llyfcjxkogcchu64ggyy

2015 Index IEEE Transactions on Automatic Control Vol. 60

2015 IEEE Transactions on Automatic Control  
., +, TAC May 2015 1204-1218 Target Assignment in Robotic Networks: Distance Optimality Guarantees and Hierarchical Strategies.  ...  Muller, M.A., +, TAC July 2015 1825-1840 On Necessity and Robustness of Dissipativity in Economic Model Predictive Control.  ... 
doi:10.1109/tac.2015.2512305 fatcat:5gut6qeomfh73fwfvehzujbr5q

How do we remember the past in randomised strategies?

Julien Cristau, Claire David, Florian Horn
2010 Electronic Proceedings in Theoretical Computer Science  
In this work, we focus on the notion of randomised strategy.  ...  In more reasonable settings, translations exist, but they require infinite memory, even in simple cases. Finally, some traditional problems becomes undecidable for the strongest type of strategies.  ...  A play π satisfies Muller(F ) if and only if the set of colours occurring infinitely often in γ(π) belongs to F . In such games, both players have pure optimal strategies with finite memory [BL69] .  ... 
doi:10.4204/eptcs.25.7 fatcat:tgrb75hs7jhc5oxns63jh6l6ue

A landscape with games in the background

I. Walukiewicz
2004 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.  
The other concerns the ways games are played, in particular probabilistic and multi-player games.  ...  An overview of applications of two player path-forming games to verification and synthesis is given.  ...  It turns out that in perfectinformation parity stochastic games the situation is much better and both players have optimal pure and memoryless strategies [20, 78] .  ... 
doi:10.1109/lics.2004.1319630 dblp:conf/lics/Walukiewicz04 fatcat:g32dgr7wfrg3zljielb4auyole

A Survey of Bidding Games on Graphs (Invited Paper)

Guy Avni, Thomas A. Henzinger, Laura Kovács, Igor Konnov
2020 International Conference on Concurrency Theory  
Specifically, bidding games, and in particular bidding games of infinite duration, have an intriguing equivalence with random-turn games in which in each turn, the player who moves is chosen randomly.  ...  A graph game is a two-player zero-sum game in which the players move a token throughout a graph to produce an infinite path, which determines the winner or payoff of the game.  ...  We restrict attention to positional strategies since in stochastic games with the objectives that we consider, existence of optimal positional strategies is well known.  ... 
doi:10.4230/lipics.concur.2020.2 dblp:conf/concur/AvniH20 fatcat:ngem4jljbfey5hg24lpsi54fsq

Page 3943 of Mathematical Reviews Vol. , Issue 87g [page]

1987 Mathematical Reviews  
Strategies with nondecreasing profit in dynamic stochastic models of the distribution of resources between production and consumption. (Russian) Optimizatsiya No. 35(52) (1985), 146-157, 160.  ...  [Muller, Eitan] (IL-HEBR-B) Characterization of constant policies in optimal control. J. Optim. Theory Appl. 48 (1986), no. 2, 315-324.  ... 
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