Lower Bounds for Complementation of ω-Automata via the Full Automata Technique
نویسنده
چکیده
In this paper, we first introduce a new lower bound technique for the state complexity of transformations of automata. Namely we suggest considering the class of full automata in lower bound analysis. Then we apply such technique to the complementation of nondeterministic ωautomata and obtain several lower bound results. Particularly, we prove anΩ((0.76n)) lower bound for Büchi complementation, which also holds for almost every complementation and determinization transformation of nondeterministic ω-automata, and prove an optimal (Ω(nk)) lower bound for the complementation of generalized Büchi automata, which holds for Streett automata as well.
منابع مشابه
Lower Bounds for Complementation of omega-Automata Via the Full Automata Technique
Vol. 4 (1:?) 2008, pp. 1–1–20 www.lmcs-online.org Submitted Jul. 25, 2007 Published Mar. ??, 2008 LOWER BOUNDS FOR COMPLEMENTATION OF ω -AUTOMATA VIA THE FULL AUTOMATA TECHNIQUE ∗ QIQI YAN Department of Computer S ien e and Engineering, Shanghai Jiao Tong University, 200240, Shanghai, P.R. China e-mail address: onta t qiqiyan. om Abstra t. In this paper, we rst introdu e a lower bound te hnique...
متن کاملAn improved lower bound for the complementation of Rabin automata Citation
Automata on infinite words (ω-automata) have wide applications in formal language theory as well as in modeling and verifying reactive systems. Complementation of ωautomata is a crucial instrument in many these applications, and hence there have been great interests in determining the state complexity of the complementation problem. However, obtaining nontrivial lower bounds has been difficult....
متن کاملA Tight Lower Bound for the Complementation of Rabin Automata
Complementing ω-automata is a crucial instrument for solving the ω-language containment problem, and therefore it has numerous applications in formal language theory, program analysis and modelchecking. There have been great interests in determining the exact complexity of the complementation problem. However, obtaining nontrivial lower bounds for the complementation problem has been difficult....
متن کاملTight Bounds for the Determinisation and Complementation of Generalised Büchi Automata
Generalised Büchi automata are Büchi automata with multiple accepting sets. They form a class of automata that naturally occurs, e.g., in the translation from LTL to ω-automata. In this paper, we extend current determinisation techniques for Büchi automata to generalised Büchi automata and prove that our determinisation is optimal. We show how our optimal determinisation technique can be used a...
متن کاملExponential Determinization for ω-Automata with Strong-Fairness Acceptance Condition
In [Saf88] an exponential determinization procedure for Büchi automata was shown, yielding tight bounds for decision procedures of some logics ([EJ88, Saf88, SV89, KT89]). In [SV89] the complexity of determinization and complementation of ω-automata was further investigated, leaving as an open question the complexity of the determinization of a single class of ω-automata. For this class of ω-au...
متن کامل