The Complexity of Iterated Reversible Computation

David Eppstein

doi:10.46298/theoretics.23.10

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arXiv · 2112.11607

The Complexity of Iterated Reversible Computation

David Eppstein

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Abstract

We study a class of functional problems reducible to computing $f^{(n)}(x)$ for inputs $n$ and $x$, where $f$ is a polynomial-time bijection. As we prove, the definition is robust against variations in the type of reduction used in its definition, and in whether we require $f$ to have a polynomial-time inverse or to be computible by a reversible logic circuit. These problems are characterized by the complexity class $\mathsf{FP}^{\mathsf{PSPACE}}$, and include natural $\mathsf{FP}^{\mathsf{PSPACE}}$-complete problems in circuit complexity, cellular automata, graph algorithms, and the dynamical systems described by piecewise-linear transformations.

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David Eppstein. 2021-12-22. The Complexity of Iterated Reversible Computation. https://doi.org/10.46298/theoretics.23.10

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