Abstract
In the context of quantum computing, reversible computations play an important role. In this paper the model of the reversible pebble game introduced by Bennett is considered. Reversible pebble game is an abstraction of a reversible computation, that allows to examine the space and time complexity for various classes of problems. We present techniques for provinglo wer and upper bounds on time and space complexity. Usingthese techniques we show a partial lower bound on time for optimal space (time for optimal space is not o(n lg n)) and a time-space tradeo. (space \( O\left( {\sqrt[k]{n}} \right) \) ) for time 2k n) for a chain of length n. Further, we show a tight optimal space bound (h+Θ(lg* h)) for a binary tree of height h and we discuss space complexity for a butterfly. By these results we give an evidence, that for reversible computations more resources are needed with respect to standard irreversible computations.
Supported in part by grant from VEGA 1/7155/20.
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Král’ovič, R. (2001). Time and Space Complexity of Reversible Pebbling. In: Pacholski, L., Ružička, P. (eds) SOFSEM 2001: Theory and Practice of Informatics. SOFSEM 2001. Lecture Notes in Computer Science, vol 2234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45627-9_26
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DOI: https://doi.org/10.1007/3-540-45627-9_26
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