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...
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...
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. We prove several results about the average-case complexity of problems in the Polynomial Hierarchy (PH). We give a connection among average-case, worst-case, and non-unif...
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...
By viewing random 3-SAT as a distributional problem, we go over some of the notions of average-case complexity that were considered in the literature. We note that for dense formul...
Abstract. In recent years, probabilistic analyses of algorithms have received increasing attention. Despite results on the average-case complexity and smoothed complexity of exact ...
Abstract. In MyCrypt 2005, Augot, Finiasz, and Sendrier proposed FSB, a family of cryptographic hash functions. The security claim of the FSB hashes is based on a coding theory pro...
Abstract. A fundamental goal of computational complexity (and foundations of cryptography) is to find a polynomial-time samplable distribution (e.g., the uniform distribution) and...
Abstract We revisit the classical QuickSort and QuickSelect algorithms, under a complexity model that fully takes into account the elementary comparisons between symbols composing ...