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- W2170056432 abstract "Finite automata on infinite words ($omega$-automata) proved to be a powerful weapon for modeling and reasoning infinite behaviors of reactive systems. Complementation of $omega$-automata is crucial in many of these applications. But the problem is non-trivial; even after extensive study during the past four decades, we still have an important type of $omega$-automata, namely Streett automata, for which the gap between the current best lower bound $2^{Omega(n lg nk)}$ and upper bound $2^{Omega(nk lg nk)}$ is substantial, for the Streett index size $k$ can be exponential in the number of states $n$. In arXiv:1102.2960 we showed a construction for complementing Streett automata with the upper bound $2^{O(n lg n+nk lg k)}$ for $k = O(n)$ and $2^{O(n^{2} lg n)}$ for $k=omega(n)$. In this paper we establish a matching lower bound $2^{Omega(n lg n+nk lg k)}$ for $k = O(n)$ and $2^{Omega(n^{2} lg n)}$ for $k = omega(n)$, and therefore showing that the construction is asymptotically optimal with respect to the $2^{Theta(cdot)}$ notation." @default.
- W2170056432 created "2016-06-24" @default.
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- W2170056432 date "2011-02-15" @default.
- W2170056432 modified "2023-09-27" @default.
- W2170056432 title "A Tight Lower Bound for Streett Complementation" @default.
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