Alternating-time stream logic for multi-agent systems
COORDINATION'08 Proceedings of the 10th international conference on Coordination models and languages
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\indent This paper presents algorithms for deciding the {\em outcome} for various classes of multiplayer games of incomplete information. A companion paper shows that these algorithms are indeed asymptotically optimal by providing matching lower bounds [APR91b]. The classes of games to which our algorithms are applicable include games which were not previously known to be decidable. We apply our algorithms to provide alternative upper bounds, and new time-space trade-offs on complexity of multiperson alternating Turing machines [PR79]. We analyze the algorithms to characterize the space complexity $S(n)$ of multiplayer games in terms of the complexity of deterministic Turing machines. In hierarchical multiplayer games each additional {\em clique} (subset of players with same information) increases the complexity of the outcome problem by a further exponential. We show that an $S (n)$ space bounded {\em k}-player game of incomplete information has a deterministic time upper bound of $k$ + 1 repeated expotentials of $S (n)$. Furthermore, $S (n)$ space bounded {\em k}-player blindfold games have deterministic space upper bound of $k$ repeated exponentials of $S (n)$. This paper proves that this exponential blow-up can occur. We also show that time bounded games do not exhibit such hierarchy. In fact, a $T (n)$ time bounded blindfold multiplayer game, as well as a $T (n)$ time bounded multiplayer game of incomplete information, has a deterministic space bound of $T (n)$.