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Content available remote On the State Complexity of Scattered Substrings and Superstrings
EN
It is proved that the set of scattered substrings of a language recognized by an n-state DFA requires a DFA with at least [formula] states (the known upper bound is 2*n), with witness languages given over an exponentially growing alphabet. For a 3-letter alphabet, scattered substrings are shown to require at least [formula] states. A similar state complexity function for scattered superstrings is determined to be exactly 2*(n-2) + 1 for an alphabet of at least n -2 letters, and strictly less for any smaller alphabet. For a 3-letter alphabet, the state complexity of scattered superstrings is at least [formula]
2
EN
Subsequence of weather elements was estimated using linear correlation method. For analyzes, the five weather elements were take under consideration: mean monthly temperature, extreme monthly temperatures (min and max), monthly sums of precipitation, as well as thermal weather seasons duration. The best correlation occurred between average temperatures of winter’s months. Only a few causes proved correlations between more far months within the years. There was pointed out a close negative correlation between duration of the succeeding seasons as well as between winter and summer duration.
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