The Conjugacy Problem in Free Solvable Groups and Wreath Products of Abelian Groups is in $${{\mathsf {T}}}{{\mathsf {C}}}^0$$

Miasnikov, Alexei; Vassileva, Svetla; Weiß, Armin

doi:10.1007/978-3-319-58747-9_20

Cited by 3 publications

(2 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The circuit complexity literature shows that many problems known to be in NC 1 were systematically placed later in TC 0 ; a nice example is integer division [BCH86,RT92] but many other interesting numerical and algebraic tasks also turn out to be in TC 0 (such as the pseudorandom function constructions of Naor and Reingold [NR04]). For many different types of groups (but not S 5 , as far as we know) their word problems are known to be in TC 0 (see [MVW17] for very recent work, with references). In fact, every natural problem that I know in NC 1 is either already NC 1 -complete under TC 0 reductions, or is already in TC 0 (there are no good candidate problems which are neither).…”

Section: Nc1 Versus Tc0mentioning

confidence: 99%

Some Estimated Likelihoods for Computational Complexity

Williams¹

2019

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

Section: Nc1 Versus Tc0mentioning

confidence: 99%

Some Estimated Likelihoods for Computational Complexity

Williams¹

2019

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…Finally, in Section 6, we discuss some open problems. This work is an extended version of the conference paper [17]. It contains all proofs, some more examples and a slightly stronger version of Theorem 4.6.…”

Section: Introductionmentioning

confidence: 99%

The Conjugacy Problem in Free Solvable Groups and Wreath Products of Abelian Groups is in TC0

2018

Self Cite

View full text Add to dashboard Cite

We show that the conjugacy problem in a wreath product A ≀ B is uniform-TC 0 -Turingreducible to the conjugacy problem in the factors A and B and the power problem in B. If B is torsion free, the power problem for B can be replaced by the slightly weaker cyclic submonoid membership problem for B. Moreover, if A is abelian, the cyclic subgroup membership problem suffices, which itself is uniform-AC 0 -many-one-reducible to the conjugacy problem in A ≀ B.Furthermore, under certain natural conditions, we give a uniform TC 0 Turing reduction from the power problem in A ≀ B to the power problems of A and B. Together with our first result, this yields a uniform TC 0 solution to the conjugacy problem in iterated wreath products of abelian groups -and, by the Magnus embedding, also in free solvable groups.

show abstract