22,066 research outputs found
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 and upper
bound , where is the state size, is the number of
Streett pairs, and can be as large as . 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 for and for ,
which matches well the lower bound obtained in \cite{CZ11a}. We also obtain a
tight upper bound for parity complementation.Comment: Corrected typos. 23 pages, 3 figures. To appear in the 20th
Conference on Computer Science Logic (CSL 2011
Self-cancellation of ephemeral regions in the quiet Sun
With the observations from the Helioseismic and Magnetic Imager aboard the
Solar Dynamics Observatory, we statistically investigate the ephemeral regions
(ERs) in the quiet Sun. We find that there are two types of ERs: normal ERs
(NERs) and self-cancelled ERs (SERs). Each NER emerges and grows with
separation of its opposite polarity patches which will cancel or coalesce with
other surrounding magnetic flux. Each SER also emerges and grows and its
dipolar patches separate at first, but a part of magnetic flux of the SER will
move together and cancel gradually, which is described with the term
"self-cancellation" by us. We identify 2988 ERs among which there are 190 SERs,
about 6.4% of the ERs. The mean value of self-cancellation fraction of SERs is
62.5%, and the total self-cancelled flux of SERs is 9.8% of the total ER flux.
Our results also reveal that the higher the ER magnetic flux is, (i) the easier
the performance of ER self-cancellation is, (ii) the smaller the
self-cancellation fraction is, and (iii) the more the self-cancelled flux is.
We think that the self-cancellation of SERs is caused by the submergence of
magnetic loops connecting the dipolar patches, without magnetic energy release.Comment: 6 pages, 4 figures, accepted for publication in ApJ
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