Satisfiability in alternating-time temporal logic

Alternating-time temporal logic (ATL) is a branching-time temporal logic that naturally describes computations of multi-agent distributed systems and multi-player games. In particular, ATL explicitly allows for the expression of coalitional ability in such situations. We present an automata-based decision procedure for ATL, by translating the satisfiability problem for ATL to the nonemptiness problem for the alternating automata on infinite trees. The key result that enables this translation is a bounded-branching tree model theorem for ATL, proving that a satisfiable in a tree model of bounded branching degree. It follows that ATL is decidable in exponential time, which is also the optimal complexity: satisfiability in CTL, a fragment of ATL, is EXPTIME-complete. The paper thus answers a fundamental logical question about ATL and provides an example of how alternation in automata may elegantly express game-like transitions.