The Complexity of Iterated Reversible Computation

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.

35 pages, 8 figures

References in corpus (2)

• A short note on graphs with long Thomason's chains
• Reflections in an octagonal mirror maze