|Résumé||Minimization of Buchi automata is an intriguing topic in automata theory,
both for a theoretical understanding of automata over infinite words, and for practical applications.
Ideally, for a given language, one would like to find an automaton recognizing it with the least number of states.
Since exact minimization is computationally hard (e.g., PSPACE-complete),
we concentrate on quotienting, which is a state-space reduction technique which works by "glueing together" certain states.
Which states can be merged is dictated by suitable preorders:
In this talk, we study fixed-word simulations, which are simulation-like preorders sound for quotienting.
We show that fixed-word simulations are coarser than previously studied simulation-like preorders,
by characterizing it with a natural (but non-trivial) ranking argument.
Our ranking construction is related to the so-called Kupferman-Vardi construction for complementing Buechi automata.