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We consider unidirectional data streams with restricted access, such asread-only and write-only streams. For read-write streams, we also introduce anew complexity measure called expansion, the ratio between the space used onthe stream and the input size. We give tight bounds for the complexity ofreversing a stream of length $n$ in several of the possible models. In theread-only and write-only model, we show that $p$-pass algorithms need memoryspace ${\Theta}(n/p)$. But if either the output stream or the input stream isread-write, then the complexity falls to ${\Theta}(n/p^2)$. It becomes$polylog(n)$ if $p = O(log n)$ and both streams are read-write. We also studythe complexity of sorting a stream and give two algorithms with smallexpansion. Our main sorting algorithm is randomized and has $O(1)$ expansion,$O(log n)$ passes and $O(log n)$ memory.

Unidirectional Input/Output Streaming Complexity of Reversal and Sorting