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In the sliding window streaming model the goal is to compute an output value that only depends on the last n symbols from the data stream. Thereby, only space sublinear in the window size n should be used. Quite often randomization is used in order to achieve this goal. In the literature, one finds two different correctness criteria for randomized sliding window algorithms: (i) one can require that for every data stream and every time instant t, the algorithm computes a correct output value with high probability, or (ii) one can require that for every data stream the probability that the algorithm computes at every time instant a correct output value is high. Condition (ii) is stronger than (i) and is called "strict correctness" in this paper. The main result of this paper states that every strictly correct randomized sliding window algorithm can be derandomized without increasing the worst-case space consumption. [ABSTRACT FROM AUTHOR]

We study the compressed representation of a ranked tree by a (string) straight-line program (SLP) for its preorder traversal, and compare it with the well-studied representation by straight-line context free tree grammars (which are also known as tree straight-line programs or TSLPs). Although SLPs may be exponentially more succinct than TSLPs, we show that many simple tree queries can still be performed efficiently on SLPs, such as computing the height of a tree, tree navigation, or evaluation of Boolean expressions. Other problems on tree traversals turn out to be intractable, e.g. pattern matching and evaluation of tree automata. These problems can be still solved in polynomial time for TSLPs. [ABSTRACT FROM AUTHOR]