The Complexity of Iterated Reversible Computation
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-t...
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| Vydáno v: | TheoretiCS Ročník 2 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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TheoretiCS Foundation e.V
26.12.2023
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| ISSN: | 2751-4838, 2751-4838 |
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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. |
|---|---|
| AbstractList | 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. 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. |
| Author | Eppstein, David |
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| Snippet | 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... 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... |
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| Title | The Complexity of Iterated Reversible Computation |
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