We give a precise definition of "generic-case complexity" and show that for a very large class of finitely generated groups the classical decision problems of group theor...
Ilya Kapovich, Alexei G. Myasnikov, Paul Schupp, V...
Abstract. We investigate the average-case complexity of decision problems for finitely generated groups, in particular the word and membership problems. Using our recent results on...
Ilya Kapovich, Alexei G. Myasnikov, Paul Schupp, V...
We examine two-cardinal problems for the class of O-minimal theories. We prove that an O-minimal theory which admits some (κ, λ) must admit every (κ , λ ). We also prove that ...
Lie group theory states that knowledge of a m-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by m the number of equations. ...
Small-bias, or -biased, spaces have found many applications in complexity theory, coding theory, and derandomization. We generalize the notion of small-bias spaces to the setting ...