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.

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Yang Cai, Ting Zhang
• Keywords: CORR 2011, Education, Lg Nk, Lower Bound, Upper Bound