Study of Circuit Complexity Using Polynomial Representations of Boolean Functions

2015 Fiscal Year Final Research Report

• Project/Area Number: 25330010
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: The University of Electro-Communications
• Principal Investigator: Tarui Jun 電気通信大学, 情報理工学(系)研究科, 准教授 (00260539)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 計算量

Outline of Final Research Achievements

We have shown that for an undirected graph with n vertices and m edges, Depth-First Search (DFS) is possible using n+o(n) bits of memory. For a directed acyclic graph, DFS is possible using n/[exp(Omega(root(log n))) ] bits of memory. We have also obtained similar results for several other graph problems. Recently, researchers are finding more and more interesting connections between Exponential-Time Hypothesis (ETH) and the time complexity of polynomial-time solvable problems. For example, it is now known that ETH implies that a truly sub-cubic algorithm does *not* exist for a certain graph problem. Our results above seem to suggest that we should investigate space-complexity analogues of this phenomena: What are the consequences of the conjecture "Problem A requires linear space" ?

Free Research Field

計算量理論