Co-ing B\"uchi Made Tight and Useful
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We solve the longstanding open problems of the blow-up involved in the
translations (when possible) of a nondeterministic B\"uchi word
automaton (NBW) to a nondeterministic co-B\"uchi word automaton (NCW)
and to a deterministic co-B\"uchi word automaton (DCW). For the NBW
to NCW translation, the currently known upper bound is $2^{O(n \log
n)}$ and the lower bound is $1.5n$. We improve the upper bound to
$n2^n$ and describe a matching lower bound of $2^{\Omega(n)}$. For the
NBW to DCW translation, the currently known upper bound is $2^{O(n
\log n)}$. We improve it to $2^{O(n)}$, which is asymptotically tight.
Both of our upper-bound constructions are based on a simple subset
construction, do not involve intermediate automata with richer
acceptance conditions, and can be implemented symbolically. We point
to numerous applications of the new constructions. In particular, they
imply a simple subset-construction based translation (when possible)
of LTL to deterministic B\"uchi word automata.