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- W2345348524 abstract "The conjugacy problem for a finitely generated group $G$ is the two-variable problem of deciding for an arbitrary pair $(u,v)$ of elements of $G$, whether or not $u$ is conjugate to $v$ in $G$. We construct examples of finitely generated, computably presented groups such that for every element $u_0$ of $G$, the problem of deciding if an arbitrary element is conjugate to $u_0$ is decidable in quadratic time but the worst-case complexity of the global conjugacy problem is arbitrary: it can be any c.e. Turing degree , can exactly mirror the Time Hierarchy Theorem, or can be $mathcal{NP}$-complete. Our groups also have the property that the conjugacy problem is generically linear time: that is, there is a linear time partial algorithm for the conjugacy problem whose domain has density $1$, so hard instances are very rare. We also consider the complexity relationship of the half-conjugacy problem to the conjugacy problem. In the last section we discuss the extreme opposite situation: groups with algorithmically finite conjugation." @default.
- W2345348524 created "2016-06-24" @default.
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- W2345348524 date "2017-10-31" @default.
- W2345348524 modified "2023-09-23" @default.
- W2345348524 title "Computational complexity and the conjugacy problem" @default.
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- W2345348524 doi "https://doi.org/10.3233/com-160060" @default.
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