Meta-Algorithms versus Circuit Lower Bounds

元算法与电路下界

• 批准号: 298363-2012
• 负责人: Kabanets, Valentine
• 金额: $ 2.48万
• 依托单位: Simon Fraser University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=571486
• 关键词: Meta; Algorithms; versus; Circuit; Lower

Computers have dramatically changed our lives. We can now efficiently solve many computational problems that would be impossible to solve without computers. Yet, many important problems still seem beyond the reach of even our most powerful super-computers. Is the apparent difficulty of these problems real (intrinsic to the problem), or these problems do have efficient algorithmic solutions that we haven't been able to discover yet? The field of computational complexity studies precisely this question: what problems require excessive computational resources (computation time, memory, etc.)? In addition to clarifying the boundary of what can be solved efficiently, identifying computationally hard problems also has important practical consequences. For instance, the security of virtually all cryptographic systems in use today (including electronic banking) relies on the unproven assumptions that certain computational problems are very hard to solve. Thus, proving that such problems are actually hard would prove that these cryptographic protocols are truly secure. One of important discoveries of modern complexity theory is the deep connection between proving the hardness of computational problems and designing efficient algorithms for related computational problems. The two tasks are like Ying and Yang of Computer Science: progress in one is impossible without progress in the other. The main goal of the proposed research is to gain better insight into this connection, and exploit it to make further progress in both computational hardness and efficient algorithm design.

计算机极大地改变了我们的生活。我们现在可以有效地解决许多没有计算机就不可能解决的计算问题。然而，许多重要的问题似乎仍然超出了我们最强大的超级计算机的能力范围。这些问题表面上的困难是真实的（问题的内在），还是这些问题确实有我们尚未发现的有效算法解决方案？