  In this paper we revisit Safra's determinization constructions for automata
on infinite words. We show how to construct deterministic automata with fewer
states and, most importantly, parity acceptance conditions. Determinization is
used in numerous applications, such as reasoning about tree automata,
satisfiability of CTL*, and realizability and synthesis of logical
specifications. The upper bounds for all these applications are reduced by
using the smaller deterministic automata produced by our construction. In
addition, the parity acceptance conditions allows to use more efficient
algorithms (when compared to handling Rabin or Streett acceptance conditions).
