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Summary: Deciding Monotonic Games
Parosh Aziz Abdulla 1 , Ahmed Bouajjani 2 , and Julien d'Orso 1
1 Uppsala University, Sweden
2 University of Paris 7, France
Abstract. In an earlier work [A
CJYK00] we presented a general frame-
work for veri cation of in nite-state transition systems, where the transi-
tion relation is monotonic with respect to a well quasi-ordering on the set
of states. In this paper, we investigate extending the framework from the
context of transition systems to that of games. We show that monotonic
games are in general undecidable. We identify a subclass of monotonic
games, called downward closed games. We provide algorithms for ana-
lyzing downward closed games subject to winning conditions which are
formulated as safety properties.
1 Introduction
One of the main challenges undertaken by the model checking community has
been to develop algorithms which can deal with in nite state spaces. In a previous
work [A
CJYK00] we presented a general framework for veri cation of in nite-
state transition systems. The framework is based on the assumption that the
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