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The CFG recognition problem is: given a context-free grammar G and a string w of length n, decide if w can be obtained from G. This is the most basic parsing question and is a core computer science problem. Valiant's parser from 1975 solves the problem in O(nO) time, where ? < 2:373 is the matrix multiplication exponent. Dozens of parsing algorithms have been proposed over the years, yet Valiant's...
The algorithmic tasks of computing the Hamming distance between a given pattern P of length m and each location in a text T of length n is one of the most fundamental algorithmic tasks in string algorithms. Karloff [IPL 1999] showed that if one is willing to suffer a 1+&#x03B5; approximation, then it is possible to solve the problem with high probability, in Õ(n/&#x03B5;2) time. Due...
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