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The Complexity of Partial-observation Stochastic Parity Games With Finite-memory Strategies [article]

Krishnendu Chatterjee and Laurent Doyen and Sumit Nain and Moshe Y. Vardi
2014 arXiv   pre-print
We improve the complexity and show that the qualitative-analysis problems for partial-observation stochastic parity games under finite-memory strategies are EXPTIME-complete; and also establish optimal  ...  The qualitative-analysis problem given a partial-observation stochastic game and a parity objective asks whether there is a strategy to ensure that the objective is satisfied with probability~1 (resp.  ...  for reachability objectives.Table 1: Complexity and memory bounds for qualitative analysis of partial-observation stochastic parity games with finite-memory strategies for player 1.  ... 
arXiv:1401.3289v1 fatcat:zzjk3omrxbbp7msyhaslzmc5f4

The Complexity of Partial-Observation Stochastic Parity Games with Finite-Memory Strategies [chapter]

Krishnendu Chatterjee, Laurent Doyen, Sumit Nain, Moshe Y. Vardi
2014 Lecture Notes in Computer Science  
The qualitative-analysis problems for partial-observation stochastic parity games were shown to be decidable with 2EXPTIME complexity for finite-memory strategies [20] ; and the exact complexity was open  ...  We improve the complexity and show that the qualitative-analysis problems for partial-observation stochastic parity games under finite-memory strategies are EXPTIME-complete; and also establish optimal  ...  Table 1 . 1 Complexity and memory bounds for qualitative analysis of partial-observation stochastic parity games with finite-memory strategies for player 1. The new results are boldfaced.  ... 
doi:10.1007/978-3-642-54830-7_16 fatcat:5vwbpd4ttfeavfhdkq6voipxnq

A survey of partial-observation stochastic parity games

Krishnendu Chatterjee, Laurent Doyen, Thomas A. Henzinger
2012 Formal methods in system design  
We consider two-player zero-sum stochastic games on graphs with ω-regular winning conditions specified as parity objectives.  ...  On the basis of information, these games can be classified as follows: (a) partialobservation (both players have partial view of the game); (b) one-sided partial-observation (one player has partial-observation  ...  The Complexity of Partial-Observation Stochastic Parity Games In this section we present a survey of results about the computational complexity and strategy complexity of different classes of partial-observation  ... 
doi:10.1007/s10703-012-0164-2 fatcat:6ptph6d4qzcm3hiqzaeik4r3pm

The Complexity of Synthesis from Probabilistic Components [article]

Krishnendu Chatterjee, Laurent Doyen, Moshe Y. Vardi
2015 arXiv   pre-print
; and (ii) belongs to UP ∩ coUP and is parity-games hard, when the specification is given directly as a parity condition on the components, improving the previously known EXPTIME upper bound.  ...  be satisfied with probability 1).  ...  Our goal is to decide the existence of finite-memory almost-sure winning strategies in partial-observation stochastic parity games.  ... 
arXiv:1502.04844v1 fatcat:h7zl6grdmzhlxfoydzbfxtjvom

The Complexity of Synthesis from Probabilistic Components [chapter]

Krishnendu Chatterjee, Laurent Doyen, Moshe Y. Vardi
2015 Lecture Notes in Computer Science  
be satisfied with probability 1).  ...  The synthesis problem asks for the automatic construction of a system from its specification.  ...  Our goal is to decide the existence of finite-memory almost-sure winning strategies in partial-observation stochastic parity games.  ... 
doi:10.1007/978-3-662-47666-6_9 fatcat:kp4z47qzkncphn4vrhjf7edetm

Solving Partial-Information Stochastic Parity Games

Sumit Nain, Moshe Y. Vardi
2013 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science  
We study one-sided partial-information 2-player concurrent stochastic games with parity objectives.  ...  We consider the problem of whether the player with partial information has a finite-memory winning strategy when the player with complete information is allowed to use an arbitrary amount of memory.  ...  Theorem 4.11: The complexity of finding if the partial-information player has a finite-memory winning strategy in a one-sided partial-information stochastic parity game is at most 2EXPTIME.  ... 
doi:10.1109/lics.2013.40 dblp:conf/lics/NainV13 fatcat:ubr5hjdryndtppdkodhuifuefm

Games with a Weak Adversary [chapter]

Krishnendu Chatterjee, Laurent Doyen
2014 Lecture Notes in Computer Science  
Our results have tight connections with partial-observation stochastic games for which we derive new complexity results. expose partial interfaces and have access to the public variables of the other processes  ...  We consider multi-player graph games with partial-observation and parity objective.  ...  Complexity of qualitative analysis (almost-sure winning) for partial-observation stochastic games with partial observation for player 1 with reachability and parity objectives.  ... 
doi:10.1007/978-3-662-43951-7_10 fatcat:lxvzfmodtnbodddkkj3b2qbnqi

Games with a Weak Adversary [article]

Krishnendu Chatterjee, Laurent Doyen
2014 arXiv   pre-print
Our results have tight connections with partial-observation stochastic games for which we derive new complexity results.  ...  We consider multi-player graph games with partial-observation and parity objective.  ...  Table 1 . 1 Complexity Reachability Parity Parity Player 2 Finite-or infinite-memory strategies Infinite-memory strategies Finite-memory strategies Player 1 Perfect More informed Perfect More informed  ... 
arXiv:1404.5453v1 fatcat:jpl36ixaobefljo3voa6cuo344

Concurrent Games and Semi-Random Determinacy

Stéphane Le Roux, Michael Wagner
2018 International Symposium on Mathematical Foundations of Computer Science  
If the winning condition satisfies some simple requirement, the existence of Player 1 winning (finitememory) strategies is equivalent to the existence of winning (finite-memory) strategies in finitely  ...  Under an additional requirement on the winning condition, the non-existence of Player 1 winning strategies from all vertices is equivalent to the existence of Player 2 stochastic strategies almost-sure  ...  If M is finite, s is called a finite-memory strategy. Note that every Player 1 strategy is implementable with memory A ω 2 . One-player games.  ... 
doi:10.4230/lipics.mfcs.2018.40 dblp:conf/mfcs/Roux18 fatcat:indrcdpaijbvdbxrgw7cok4ed4

Qualitative Analysis of Partially-Observable Markov Decision Processes [chapter]

Krishnendu Chatterjee, Laurent Doyen, Thomas A. Henzinger
2010 Lecture Notes in Computer Science  
An observation-based strategy relies on partial information about the history of a play, namely, on the past sequence of observations.  ...  Second, we present optimal bounds (matching upper and lower bounds) on the memory required by pure and randomized observation-based strategies for the qualitative analysis of POMDP s with parity objectives  ...  The optimal memory bounds for strategies in POMDPs are as follows. 1.  ... 
doi:10.1007/978-3-642-15155-2_24 fatcat:l5eaex4525bubhbo4fzen6qiey

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.  ...  Given a game graph G and a strategy in Σ ∪ Π with finite memory M, the strategy can be interpreted as a memoryless strategy in the synchronous product G × M of the game graph G with the memory M.  ... 
doi:10.1016/j.jcss.2011.05.002 fatcat:267iudbahzf4tdef2fo573l3ie

Stochastic Parity Games on Lossy Channel Systems [chapter]

Parosh Aziz Abdulla, Lorenzo Clemente, Richard Mayr, Sven Sandberg
2013 Lecture Notes in Computer Science  
The above two steps yield an algorithm to decide parity games in the case when the players are restricted to finite memory strategies.  ...  The correctness proof here is more involved than in the non-stochastic case of [Zie98]; we rely on the existence of a finite attractor and the restriction of the players to use finite-memory strategies  ...  PARITY CONDITIONS We describe a scheme for solving stochastic parity games with almost-sure winning conditions on infinite graphs, under the conditions that the game has a finite attractor (as defined  ... 
doi:10.1007/978-3-642-40196-1_29 fatcat:tu7smttaqrbz7fit6iosx3vivy

Emptiness Of Alternating Tree Automata Using Games With Imperfect Information

Nathanaël Fijalkow, Sophie Pinchinat, Olivier Serre, Marc Herbstritt
2013 Foundations of Software Technology and Theoretical Computer Science  
result for stochastic games played over infinite graphs.  ...  Indeed, we directly reduce the emptiness problem to solving an imperfect information two-player parity game.  ...  Imperfect Information Stochastic Parity Games In the following we introduce a quite restrictive class of games with imperfect information which is essentially a stochastic version of the model in [10]  ... 
doi:10.4230/lipics.fsttcs.2013.299 dblp:conf/fsttcs/FijalkowPS13 fatcat:r52v4d7jwnhvrdjvjheutpftfm

Life Is Random, Time Is Not: Markov Decision Processes with Window Objectives

Thomas Brihaye, Florent Delgrange, Youssouf Oualhadj, Mickael Randour, Michael Wagner
2019 International Conference on Concurrency Theory  
Our work paves the way to a wide use of the window mechanism in stochastic models.  ...  The window mechanism was introduced by Chatterjee et al. [17] to strengthen classical game objectives with time bounds.  ...  Our goal is to lift the theory of window games to the stochastic context.  ... 
doi:10.4230/lipics.concur.2019.8 dblp:conf/concur/BrihayeDOR19 fatcat:v4qxzfut3rfuhg3tdpkqr3ctpm

Probabilistic Model Checking and Autonomy [article]

Marta Kwiatkowska, Gethin Norman, David Parker
2021 arXiv   pre-print
This includes fully observable and partially observable Markov decision processes, as well as turn-based and concurrent stochastic games, together with associated probabilistic temporal logics.  ...  This method has recently been extended to multi-agent systems that exhibit competitive or cooperative behaviour modelled via stochastic games and synthesis of equilibria strategies.  ...  DISCLOSURE STATEMENT The authors are not aware of any affiliations, memberships, funding, or financial holdings that might be perceived as affecting the objectivity of this review. LITERATURE CITED  ... 
arXiv:2111.10630v1 fatcat:ckaniytpargkpcug52qvwgh3iy
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