Abstract
special issue in honor of Laci Babai's 60th birthday: Combinatorics, Groups, Algorithms, and Complexity We prove that the extended equivalence problem is solvable in polynomial time for finite nilpotent groups, and coNP-complete, otherwise. We prove that the extended equation solvability problem is solvable in polynomial time for finite nilpotent groups, and NP-complete, otherwise.
Highlights
The algorithmic aspects of the equivalence problem and the equation solvability problem have received increasing attention in the past two decades
The complexity of the equivalence and equation solvability problems have been thoroughly investigated for finite classical algebras, e.g. for finite rings Burris and Lawrence (1993); Hunt and Stearns (1990); Lawrence and Willard (1997); Szabó and Vértesi (2011), for finite groups Burris and Lawrence (2004); Goldmann and Russell (2002); Horváth (2011); Horváth et al (2007); Horváth and Szabó (2006), or for finite semigroups and monoids Almeida et al (2009); Kisielewicz (2004); Klíma (2004, 2009); Plescheva and Vértesi (2006); Seif and Szabó (2006)
To further investigate whether or not additional operations can affect the complexity of the equivalence and equation solvability problems, we introduce their extended version for finite groups
Summary
The algorithmic aspects of the equivalence problem and the equation solvability problem have received increasing attention in the past two decades. The complexity of the equivalence and equation solvability problems have been thoroughly investigated for finite classical algebras, e.g. for finite rings Burris and Lawrence (1993); Hunt and Stearns (1990); Lawrence and Willard (1997); Szabó and Vértesi (2011), for finite groups Burris and Lawrence (2004); Goldmann and Russell (2002); Horváth (2011); Horváth et al (2007); Horváth and Szabó (2006), or for finite semigroups and monoids Almeida et al (2009); Kisielewicz (2004); Klíma (2004, 2009); Plescheva and Vértesi (2006); Seif and Szabó (2006) The complexity of these questions is determined with respect to the length of the input term or polynomial expressions.
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