In this paper, we study the structure of underlying automata based constructions for solving the LTL realizability problem. We show how to reduce the LTL realizability problem to a game with an observer which checks that the game visits a bounded number of times accepting states of a universal co-Büchi word automaton. We show that such an observer can be made deterministic and that this deterministic observer has a nice structure which can be exploited by an incremental algorithm that

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... s antichains of game positions. We have implemented this new algorithm and our first results are very encouraging. 1 Technically, we could have started with Player I, for modeling reason it is conservative to start with Player O. Proposition 5. Given a graph G = (V, E), we can construct in deterministic polynomial time a UK CW A, with K = 0, and an antichain L such that IND(G) =↓ Pre I (Pre O (Pre O ((L))).