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Electronic Notes in Theoretical Computer Science
Volume 43, May 2001, Pages 15-33
Formal Methods Elsewhere (a Satellite Workshop of FORTE-PSTV-2000 devoted to applications of formal methods to areas other than communication protocols and software engineering)
 
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doi:10.1016/S1571-0661(04)80892-2    How to Cite or Link Using DOI (Opens New Window)
Copyright © 2001 Published by Elsevier B.V.

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Can American Checkers be Solved by Means of Symbolic Model Checking?star, open

Michael Baldamusa, Klaus Schneidera, Michael Wenza and Roberto Zillera

aUniversity of Karlsruhe, Institute for Computer Desgin and Fault Tolerance, Formal Methods Grouphttp://goethe.ira.uka.de/fmg

Available online 28 September 2004.

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Abstract

Symbolic model checking has become a successful technique for verifying large finite state systems up to more than 1020 states. The key idea of this method is that extremely large sets can often be efficiently represented with propositional formulas. Most tools implement these formulas by means of binary decision diagrams (BDDs), which have therefore become a key data structure in modern VLSI CAD systems.

Some board games like American checkers have a state space whose size is well within the range of state space sizes that have been tackled by symbolic model checking. Moreover, the question whether there is a winning strategy in these games can be reduced to two simple μcalculus formulas. Hence, the entire problem to solve such games can be reduced to simple μcalculus model checking problems.

In this paper, we show how to model American checkers as a finite state system by means of BDDs. We moreover specify the existence of winning strategies for both players by simple μ-calculus formulas. Further still, we report on our experimental results with our own model checking tool, and we describe some powerful improvements that we have found in trying to solve the game.


Electronic Notes in Theoretical Computer Science
Volume 43, May 2001, Pages 15-33
Formal Methods Elsewhere (a Satellite Workshop of FORTE-PSTV-2000 devoted to applications of formal methods to areas other than communication protocols and software engineering)
 
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