Special Issue On Worst-case Versus Average-case Complexity Editors' Foreword

Oded Goldreich, Salil Vadhan
2007 Computational Complexity  
Average-case complexity, which examines the tractability of computational problems on 'random instances,' is a major topic in complexity theory with at least two distinct motivations. On one hand, it may provide a more realistic model than worst-case complexity for the problem instances actually encountered in practice. On the other hand, it provides us with methods to generate hard instances, allowing us to harness intractability for useful ends such as cryptography and derandomization. These
more » ... wo motivations are actually supported by a variety of different notions of average-case complexity (surveyed in [17, 13, 6] ) and relating these notions is an important direction for research in the area. An even more ambitious goal is to understand the relationship between average-case complexity and worst-case complexity, e.g., whether NP = P implies that NP has problems that are hard on average. In recent years, there has been substantial progress on this front. This special issue aims to present a small sample of papers that are representative of the different types of results that have been obtained:
doi:10.1007/s00037-007-0232-y fatcat:ngds2ex4njfyfaza2xcqqqbx3y