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...
Abstract. We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be a...
Abstract. Motivated by a study of Zimand (22nd CCC, 2007), we consider the average-case complexity of property testing (focusing, for clarity, on testing properties of Boolean stri...
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...