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Simple Algorithm for Simple Timed Games

Yasmina Abdeddaim, Eugène Asarin, Mihaela Sighireanu
2009 2009 16th International Symposium on Temporal Representation and Reasoning  
We search to solve finite-horizon reachability games on Task TGA by building strategies in the form of Simple Temporal Networks with Uncertainty (STNU).  ...  A practical consequence of this result is a fully forward algorithm for building STNU strategies. Potential applications of this work are planning and scheduling under temporal uncertainty.  ...  The algorithm testing when an STNU is a winning strategy for a simple game is given on Figure 4 .  ... 
doi:10.1109/time.2009.14 dblp:conf/time/AbdeddaimAS09 fatcat:quaalvp4xnfgvnniwkoguuyslm

Simple Recursive Games [article]

Daniel Andersson, Kristoffer Arnsfelt Hansen, Peter Bro Miltersen, Troels Bjerre Sorensen
2007 arXiv   pre-print
We study the complexity of solving simple recursive games and obtain an almost-linear time comparison-based algorithm for computing an equilibrium of such a game.  ...  The existence of a linear time comparison-based algorithm remains an open problem.  ...  We are indebted to Mike Paterson for his contributions to this work. We would also like to thank Uri Zwick and Gerth Brodal for helpful discussions.  ... 
arXiv:0711.1055v1 fatcat:ch7rv3bxpjbqfakoz6xcv6qfqe

Forms of representation for simple games: Sizes, conversions and equivalences

Xavier Molinero, Fabián Riquelme, Maria Serna
2015 Mathematical Social Sciences  
This paper surveys different forms of representation of simple games, and those for some of their subfamilies like regular games and weighted games.  ...  Simple games are cooperative games in which the benefit that a coalition may have is always binary, i.e., a coalition may either win or loose.  ...  Xavier Molinero has been partially supported by grant MTM2012-34426/FEDER from the Spanish Ministry for Economy and Competitiveness.  ... 
doi:10.1016/j.mathsocsci.2015.04.008 fatcat:edomummiqrgbnh5synzydz65sm

The Complexity of Simple Stochastic Games [article]

Jonas Dieckelmann
2007 arXiv   pre-print
In this paper we survey the computational time complexity of assorted simple stochastic game problems, and we give an overview of the best known algorithms associated with each problem.  ...  In her paper about algorithms for simple stochastic games, Condon [5] presents a "worst case" example for the successive approximation algorithm in form of a special game graph, where the algorithm takes  ...  A particularly simple algorithm of this class is the one of Hoffman & Karp [11] , for which a worst case running time of O(2 n /n) is established.  ... 
arXiv:0704.2779v1 fatcat:i7ll6jb43re3pni76yu3lhpqkm

Computing Probabilistic Bisimilarity Distances via Policy Iteration

Qiyi Tang, Franck Van Breugel, Marc Herbstritt
2016 International Conference on Concurrency Theory  
A modification of a basic version of their algorithm for a labelled Markov chain is shown to be the policy iteration algorithm applied to the corresponding simple stochastic game.  ...  Furthermore, it is shown that this algorithm takes exponential time in the worst case.  ...  The authors would like to thank Norm Ferns for extensive discussions. The authors are also grateful to the referees for their constructive feedback.  ... 
doi:10.4230/lipics.concur.2016.22 dblp:conf/concur/TangB16 fatcat:ndxvs5qrjbgozp5jitxypdmy3u

New Algorithms for Solving Simple Stochastic Games

Rafał Somla
2005 Electronical Notes in Theoretical Computer Science  
It is an open problem, whether simple stochastic games can be solved in polynomial time. Our algorithms determine the optimal expected payoffs in the game.  ...  We present new algorithms for determining optimal strategies for two-player games with probabilistic moves and reachability winning conditions.  ...  Summary We present two algorithms for determining optimal values and strategies in a simple stochastic game.  ... 
doi:10.1016/j.entcs.2004.07.008 fatcat:tthbkdjtanhbjigtqnrqhdhqoi

Solving simple stochastic games with few coin toss positions [article]

Rasmus Ibsen-Jensen, Peter Bro Miltersen
2012 arXiv   pre-print
Gimbert and Horn gave an algorithm for solving simple stochastic games with running time O(r!  ...  While the algorithm is simple, the analysis leading to this time bound is involved, using techniques of extremal combinatorics to identify worst case instances for the algorithm.  ...  Our algorithm for solving simple stochastic games with few coin toss positions is the algorithm of Figure 1 . [1] for solving deterministic graphical games.  ... 
arXiv:1112.5255v3 fatcat:qibanfhe5ff45am7e6qtny3ivq

Combinatorial Structures to Construct Simple Games and Molecules

Xavier Molinero
2017 International Journal of Theoretical and Applied Mathematics  
First, we characterize simple games as influence games using influence graphs. It let us to modeling simple games as combinatorial structures (from the viewpoint of structures or graphs).  ...  In particular, we establish the bases to represent some simple games, defined as influence games, and molecules, defined from atoms, by using combinatorial structures.  ...  The algorithms to generate combinatorial structures (simple games or molecules) should be analyzed to use genetic algorithms [16] , [28] , (meta-) heuristic algorithms [1] , [27] , [24] , [13] or  ... 
doi:10.11648/j.ijtam.20170302.16 fatcat:ptdekqloo5ecvjo7dnqp7srx3i

On the Complexity of the Decisive Problem in Simple, Regular and Weighted Games [article]

Andreas Polyméris, Fabián Riquelme
2013 arXiv   pre-print
We show that this concept can naturally be represented in the context of hypergraph theory, and that decisiveness can be decided for simple games in quasi-polynomial time, and for regular and weighted  ...  games in polynomial time.  ...  Algorithm 1 IsWeighted Input: The irredundant kernel H := µ(W) of a simple game Γ := (A, W).  ... 
arXiv:1303.7122v2 fatcat:reydh4657vbjhiop5a6hyvyhtq

Computing Probabilistic Bisimilarity Distances for Probabilistic Automata

Giorgio Bacci, Giovanni Bacci, Kim G. Larsen, Radu Mardare, Qiyi Tang, Franck Van Breugel, Michael Wagner
2019 International Conference on Concurrency Theory  
The characterization gives us an algorithm to compute the distances by applying Condon's simple policy iteration on these games.  ...  Our games may be non-stopping in general, yet we are able to prove termination for this extended class of games.  ...  [12] as the solution of a simple stochastic game. Starting from it, we designed algorithms for computing the distances based on Condon's simple policy iteration algorithm.  ... 
doi:10.4230/lipics.concur.2019.9 dblp:conf/concur/BacciBLMTB19 fatcat:qjnelkx5czexvnbk5ntoutbnsq

Minimizing Simple and Cumulative Regret in Monte-Carlo Tree Search [chapter]

Tom Pepels, Tristan Cazenave, Mark H. M. Winands, Marc Lanctot
2014 Communications in Computer and Information Science  
Recently, simple regret has been proposed as a new criterion for assessing the performance of both MAB [2, 6] and MCTS [7, 9, 18] algorithms.  ...  Recently, simple regret, i.e., the regret of not recommending the best action, has been proposed as an alternative to cumulative regret in MCTS, i.e., regret accumulated over time.  ...  Acknowledgments This work is partially funded by the Netherlands Organisation for Scientific Research (NWO) in the framework of the project Go4Nature, grant number 612.000.938.  ... 
doi:10.1007/978-3-319-14923-3_1 fatcat:opso7iiy4faenogqefylqelxui

An Exploration of HCI Design Features and Usability Techniques in Gaming

Venkata Krishna
2013 IOSR Journal of Computer Engineering  
This Conference paper explores the human computer interaction design features relating to gaming industry.  ...  HCI design features of Simple Sudoku and Contemporary HCI Expectations are also discussed. And suggestions are given to develop the Simple Sudoku as per HCI standards and expectations.  ...  use of different algorithmic approaches for solving puzzles of Simple Sudoku etc.  ... 
doi:10.9790/0661-1535357 fatcat:z736pydeivcafmk527l3dc3eqy

New Results on Simple Stochastic Games [chapter]

Decheng Dai, Rong Ge
2009 Lecture Notes in Computer Science  
This algorithm is the fastest known algorithm when |V R | = ω(log n) and |V R | = o( min |V min |, |Vmax|) and it works for general (non-stopping) simple stochastic games.  ...  of simple stochastic games.  ...  Fast Algorithm for SSGs with few random vertices An interesting case for solving simple stochastic games is when there are a few random vertices.  ... 
doi:10.1007/978-3-642-10631-6_102 fatcat:3cns6dgg7rcslasflzks2osige

Solving Weighted Voting Game Design Problems Optimally: Representations, Synthesis, and Enumeration [article]

Bart de Keijzer and Tomas B. Klos and Yingqian Zhang
2013 arXiv   pre-print
We survey algorithms and impossibility results for the synthesis problem, i.e., converting a representation of a simple game into another representation.  ...  Then, we proceed by studying the problem of enumerating the set of weighted voting games. We present first a naive algorithm for this, running in doubly exponential time.  ...  Because this algorithm is central to our approach for solving the PVGD-problem, we will here restate the algorithm in terms of simple games, and we will give a proof of its correctness and polynomial time  ... 
arXiv:1204.5213v3 fatcat:ysl4t7fl5jc4hotmeem2pupkte

Spanning connectivity games [article]

Haris Aziz, Oded Lachish, Mike Paterson, Rahul Savani
2009 arXiv   pre-print
It is also shown that for any reasonable representation of a simple game, a polynomial time algorithm to compute the Shapley-Shubik indices implies a polynomial time algorithm to compute the Banzhaf indices  ...  As a corollary, computing the Shapley value is #P-complete for simple games represented by the set of minimal winning coalitions, Threshold Network Flow Games, Vertex Connectivity Games and Coalitional  ...  Acknowledgements Partial support for this research was provided by DIMAP (the Centre for Discrete Mathematics and its Applications), which is funded by the UK EPSRC under grant EP/D063191/1.  ... 
arXiv:0906.3643v1 fatcat:o2t453gl5zeq5kfn626wxh6btu
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