Eliminating Unbounded Search In Computable Algebra

Klaimullin, Melnikov and Ng [KMNa] have recently suggested a new systematic approach to algorithms in algebra which is intermediate between computationally feasible algebra [CR91, KNRS07] and abstract computable structure theory [AK00, EG00]. In this short survey we discuss some of the key results and ideas of this new topic [KMNa, KMNc, KMNb]. We also suggest several open problems.