  In the mid 80s, Lichtenstein, Pnueli, and Zuck proved a classical theorem
stating that every formula of Past LTL (the extension of LTL with past
operators) is equivalent to a formula of the form $\bigwedge_{i=1}^n
\mathbf{G}\mathbf{F}\, \varphi_i \vee \mathbf{F}\mathbf{G}\, \psi_i $, where
$\varphi_i$ and $\psi_i$ contain only past operators. Some years later, Chang,
Manna, and Pnueli built on this result to derive a similar normal form for LTL.
Both normalization procedures have a non-elementary worst-case blow-up, and
follow an involved path from formulas to counter-free automata to star-free
regular expressions and back to formulas. We improve on both points. We present
direct and purely syntactic normalization procedures for LTL, yielding a normal
form very similar to the one by Chang, Manna, and Pnueli, that exhibit only a
single exponential blow-up. As an application, we derive a simple algorithm to
translate LTL into deterministic Rabin automata. The algorithm normalizes the
formula, translates it into a special very weak alternating automaton, and
applies a simple determinization procedure, valid only for these special
automata.
