This paper takes the next step in developing the theory of average case complexity initiated by Leonid A Levin. Previous works Levin 84, Gurevich 87, Venkatesan and Levin 88] have...
Levin introduced an average-case complexity measure, based on a notion of \polynomialon average," and de ned \average-case polynomial-time many-one reducibility" amongra...
For the worst-case complexity measure, if P = NP, then P = OptP, i.e., all NP optimization problems are polynomial-time solvable. On the other hand, it is not clear whether a simi...
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...