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Abstract

We present a randomized and a deterministic data structure for maintaining a dynamic family of sequences under equality--tests of pairs of sequences and creations of new sequences by joining or splitting existing sequences. Both data structures support equality--tests in $O(1)$ time. The randomized version supports new sequence creations in $O(\log^2 n)$ expected time where $n$ is the length of the sequence created. The deterministic solution supports sequence creations in $O(\log n(\log m \log^* m + \log n))$ time for the $m$--th operation.