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We show an efficient pattern matching algorithm for strings that are succinctly described in terms of straight-line programs, in which the constants are symbols and the only operation is the concaten...ation. In this paper, both text $ T $ and pattern $ P $ are given by straight-line programs $ \tau $ and $ \rho $. The length of the text $ T $ (pattern $ P $, resp.) may grows exponentially with respect to its description size $ mid \tau mid = n (mid \rho mid = m, resp.) $. We show a new combinatorial property concerning with the periodic occurrences in a text. Based on this property, we develop an $ O(n^2m^2) $ time algorithm using $ O(nm) $ space, which outputs a compact representation of all occurrences of $ P $ in $ T $. This is superior to the algorithm proposed by Karpinski et al.[11], which runs in $ O((n + m)^4log (n + m)) $ time using $ O((n+m)^3) $ space, and finds only one occurrence. Moreover, our algorithm is much simpler than theirs.show more
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