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

Singly Exponential Translation of Alternating Weak B\"uchi Automata to Unambiguous B\"uchi Automata