Complementation Constructions for Nondeterministic Automata on Infinite Words ============================================================================= The complementation problem for nondeterministic automata on infinite words has numerous applications in formal verification. In particular, the language-containment problem, to which many verification problems is reduced, involves complementation. Traditional optimal complementation constructions are quite complicated and have not been implemented. Recently, we analyzed runs of co-Büchi and generalized co-Büchi automata and used the analysis to describe simpler optimal complementation constructions for Büchi and generalized Büchi automata. In this work, we extend the analysis to Rabin and Streett automata, and use the analysis to describe novel, simple, and optimal complementation constructions for them.