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Monotonic and Downward Closed Games* PAROSH AZIZ ABDULLA, Uppsala University, Sweden.
 

Summary: Monotonic and Downward Closed Games*
PAROSH AZIZ ABDULLA, Uppsala University, Sweden.
E-mail: parosh@it.uu.se
AHMED BOUAJJANI and JULIEN D'ORSO, University of Paris 7, France.
Abstract
In an earlier work [Abdulla et al. (2000, Information and Computation, 160, 109127)] we presented a general framework for
verification of infinite-state transition systems, where the transition relation is monotonic with respect to a well quasi-ordering
on the set of states. In this article, we investigate extending the framework from the context of transition systems to that of
games with infinite state spaces. We show that monotonic games with safety winning conditions are in general undecidable.
In particular, we show this negative results for games which are defined over Petri nets. We identify a subclass of monotonic
games, called downward closed games.We provide algorithms for analysing downward closed games subject to safety winning
conditions. We apply the algorithm to games played on lossy channel systems. Finally, we show that weak parity games are
undecidable for the above classes of games.
Keywords: infinite-state games, lossy channel systems, Vector Addition Systems, Petri nets.
1 Introduction
One of the main challenges undertaken by the model checking community has been to develop
algorithms which can deal with infinite state spaces. In a previous work [1], we presented a general
framework for verification of infinite-state transition systems. The framework is based on the
assumption that the transition relation is monotonic with respect to a well quasi-ordering on the
set of states (configurations). The framework has been used both to give uniform explanations of

  

Source: Abdulla, Parosh Aziz - Department of Information Technology, Uppsala Universitet

 

Collections: Computer Technologies and Information Sciences