The Complexity of Iterated Reversible Computation
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We define a complexity class 𝖨𝖡 as the 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. We relate 𝖨𝖡 to other standard complexity classes, and demonstrate its applicability by finding natural 𝖨𝖡-complete problems in circuit complexity, cellular automata, graph algorithms, and the dynamical systems described by piecewise-linear transformations.
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