  We introduce a method for translating an alternating weak B\"uchi automaton
(AWA), which corresponds to a Linear Dynamic Logic (LDL) formula, to an
unambiguous B\"uchi automaton (UBA). Our translations generalise constructions
for Linear Temporal Logic (LTL), a less expressive specification language than
LDL. In classical constructions, LTL formulas are first translated to
alternating \emph{very weak} automata (AVAs) -- automata that have only
singleton strongly connected components (SCCs); the AVAs are then handled by
efficient disambiguation procedures. However, general AWAs can have larger
SCCs, which complicates disambiguation. Currently, the only available
disambiguation procedure has to go through an intermediate construction of
nondeterministic B\"uchi automata (NBAs), which would incur an exponential
blow-up of its own. We introduce a translation from \emph{general} AWAs to UBAs
with a \emph{singly} exponential blow-up, which also immediately provides a
singly exponential translation from LDL to UBAs. Interestingly, the complexity
of our translation is \emph{smaller} than the best known disambiguation
algorithm for NBAs (broadly $(0.53n)^n$ vs. $(0.76n)^n$), while the input of
our construction can be exponentially more succinct.
