Tight Upper Bounds for Streett and Parity Complementation

Complementation of finite automata on infinite words is not only a fundamental problemin automata theory, but also serves as a cornerstone for solving numerous decision problemsin mathematical logic, model-checking, program analysis and verification. For Streett comple-mentation, a significant gap exists between the current lower bound 2 lgnk) and upper bound2 lg , where n is the state size, k is the number of Streett pairs, and k can be as large as2. Determining the complexity of Streett complementation has been an open question since thelate ’80s. In this paper show a complementation construction with upper bound 2 lgn+nk lg k)for k = O(n) and 22 lgn) for k = ω(n), which matches well the lower bound obtained in [3].We also obtain a tight upper bound 2 lgn) for parity complementation.