Logspace and compressed-word computations in nilpotent groups
Jeremy Macdonald, Alexei Myasnikov, Andrey Nikolaev, Svetla Vassileva
Abstract
For finitely generated nilpotent groups, we employ Mal’cev coordinates to solve several classical algorithmic problems efficiently. Computation of normal forms, the membership problem, the conjugacy problem, and computation of presentations for subgroups are solved using only logarithmic space and quasilinear time. Logarithmic space presentation-uniform versions of these algorithms are provided. Compressed-word versions of the same problems, in which each input word is provided as a straight-line program, are solved in polynomial time.
Topics & Concepts
MathematicsConjugacy problemNilpotentWord (group theory)ComputationLogarithmConjugacy classWord problem (mathematics education)PolynomialSpace (punctuation)Algebra over a fieldDiscrete mathematicsPure mathematicsArithmeticAlgorithmMathematical analysisComputer scienceGeometryOperating systemGeometric and Algebraic TopologyFinite Group Theory Researchsemigroups and automata theory