Analyzing Old Games with Modern Techniques: Probabilistic Model Checking Using SCOOP and PRISM

Model checkers can be used to solve mathematical problems, without the need of having prior knowledge on the technical solution to those problems. This paper focuses on the practical usage of the tool SCOOP, which uses several optimization techniques for state space reduction in probabilistic automata. SCOOP can be used in collaboration with probabilistic model checkers such as PRISM to solve a given probabilistic problem, so that a manual approach is unnecessary. Three case studies are examined to show how to use SCOOP and, more importantly, to give an understanding of when to choose a model checking approach instead of trying to calculate a solution manually. The case studies are specically focused on probabilistic games because of the ease of understanding and the freedom of applying variations. The N -Player ruin, Yahtzee and the Game of the Goose are the games that are analyzed. Scaling and other alterations are applied to nd out to what extent these aect the state space and time used as well as the mathematical interpretation. The usage of SCOOP’s optimization techniques is investigated to nd out if and how these reduce the state space and time used to solve the problems more eciently. The results will show that in some cases, a model checking approach provides results that are not realistically obtainable with alternative techniques.

[1]  Jan Friso Groote,et al.  The Syntax and Semantics of μCRL , 1995 .

[2]  The gambler's ruin problem with n players and asymmetric play , 1999 .

[3]  Christel Baier,et al.  PROBMELA: a modeling language for communicating probabilistic processes , 2004, Proceedings. Second ACM and IEEE International Conference on Formal Methods and Models for Co-Design, 2004. MEMOCODE '04..

[4]  Phil Woodward,et al.  Yahtzee®: The Solution , 2003 .

[5]  Yvik Swan.  On two unsolved problems in probability , 2007 .

[6]  F. Stern,et al.  The asymmetric n-player gambler's ruin problem with equal initial fortunes , 2004, Adv. Appl. Math..

[7]  Mark Timmer.  SCOOP: A Tool for SymboliC Optimisations of Probabilistic Processes , 2011, 2011 Eighth International Conference on Quantitative Evaluation of SysTems.

[8]  Nikolay V. Shilov,et al.  Puzzles for Learning Model Checking, Model Checking for Programming Puzzles, Puzzles for Testing Model Checkers , 2001, Electron. Notes Theor. Comput. Sci..

[9]  Jaco van de Pol,et al.  Confluence Reduction for Probabilistic Systems , 2011, TACAS.

[10]  Andrew Hinton,et al.  PRISM: A Tool for Automatic Verification of Probabilistic Systems , 2006, TACAS.

[11]  Joost-Pieter Katoen,et al.  A linear process-algebraic format with data for probabilistic automata , 2012, Theor. Comput. Sci..

[12]  Howard Bowman.  Preface: Volume 43 , 2001 .

[13]  Jaco van de Pol,et al.  State Space Reduction of Linear Processes Using Control Flow Reconstruction , 2009, ATVA.