Tight Upper Bounds for Streett and Parity Complementation

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Tight Upper Bounds for Streett and Parity Complementation
Complementation of finite automata on infinite words is not only a fundamental problem in automata theory, but also serves as a cornerstone for solving numerous decision problems in mathematical logic, model-checking, program analysis and verification. For Streett complementation, a significant gap exists between the current lower bound 2Ω(n lg nk) and upper bound 2O(nk lg nk) , where n is the state size, k is the number of Streett pairs, and k can be as large as 2n . Determining the complexity of Streett complementation has been an open question since the late ’80s. In this paper show a complementation construction with upper bound 2O(n lg n+nk lg k) for k = O(n) and 2O(n2 lg n) for k = ω(n), which matches well the lower bound obtained in [3]. We also obtain a tight upper bound 2O(n lg n) for parity complementation.
Yang Cai, Ting Zhang
Added 19 Aug 2011
Updated 19 Aug 2011
Type Journal
Year 2011
Where CORR
Authors Yang Cai, Ting Zhang
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