Tight Upper Bounds for Streett and Parity Complementation

Authors Yang Cai, Ting Zhang

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Yang Cai
Ting Zhang

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Yang Cai and Ting Zhang. Tight Upper Bounds for Streett and Parity Complementation. In Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 12, pp. 112-128, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)


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 2^{Omega(n*log(n*k))} and upper bound 2^{O(n*k*log(n*k))}, where n is the state size, k is the number of Streett pairs, and k can be as large as 2^{n}. Determining the complexity of Streett complementation has been an open question since the late 80's. In this paper we show a complementation construction with upper bound 2^{O(n*log(n)+n*k*log(k))} for k=O(n) and 2^{O(n^{2}*log(n))} for k=Omega(n), which matches well the lower bound obtained in the paper arXiv:1102.2963. We also obtain a tight upper bound 2^{O(n*log(n))} for parity complementation.
  • Streett automata
  • omega-automata
  • parity automata
  • complementation
  • upper bounds


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