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 $2^{\Omega(n\lg nk)}$ and upper bound $2^{O(nk\lg nk)}$, 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 '80s. In this paper show a complementation construction with upper bound $2^{O(n \lg n+nk \lg k)}$ for $k = O(n)$ and $2^{O(n^{2} \lg n)}$ for $k = \omega(n)$, which matches well the lower bound obtained in \cite{CZ11a}. We also obtain a tight upper bound $2^{O(n \lg n)}$ for parity complementation.Comment: Corrected typos. 23 pages, 3 figures. To appear in the 20th Conference on Computer Science Logic (CSL 2011

Homologous Flux Ropes Observed by SDO/AIA

We firstly present the Solar Dynamics Observatory observations of four homologous flux ropes in active region (AR) 11745 on 2013 May 20-22. The four flux ropes are all above the neutral line of the AR, with endpoints anchoring at the same region, and have the generally similar morphology. For the first three flux ropes, they rose up with a velocity of less than 30 km s$^{-1}$ after their appearances, and subsequently their intensities at 131 {\AA} decreased and the flux ropes became obscure. The fourth flux rope erupted ultimately with a speed of about 130 km s$^{-1}$ and formed a coronal mass ejection. The associated filament showed an obvious anti-clockwise twist motion at the initial stage, and the twist was estimated at 4$\pi$. This indicates that kink instability possibly triggers the early rise of the fourth flux rope. The activated filament material was spatially within the flux rope and they showed consistent evolution in their early stages. Our findings provide new clues for understanding the characteristics of flux ropes. Firstly, there are multiple flux ropes that are successively formed at the same location during an AR evolution process. Secondly, a slow-rise flux rope does not necessarily result in a CME, and a fast-eruption flux rope results in a CME.Comment: 15 pages, 5 figures, accepted in ApJ

Measurement-induced nonlocality in arbitrary dimensions in terms of the inverse approximate joint diagonalization

Here we focus on the measurement induced nonlocality and present a redefinition in terms of the skew information subject to a broken observable. It is shown that the obtained quantity possesses an obvious operational meaning, can tackle the noncontractivity of the measurement induced nonlocality and has analytic expressions for many quantum states. Most importantly, an inverse approximate joint diagonalization algorithm, due to its simplicity, high efficiency, stability, and state independence, is presented to provide almost analytic expressions for any quantum state, which can also shed light on other aspects in physics