2012 Fiscal Year Final Research Report
Propositional Proof Complexity: Analysis fromComputational Complexity Perspectives
| Project/Area Number |
22500012
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Fundamental theory of informatics
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| Research Institution | The University of Electro-Communications |
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Principal Investigator |
TARUI Jun 電気通信大学, 大学院・情報理工学研究科, 准教授 (00260539)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 計算量理論 / 計算の複雑さ / 証明の複雑さ / ストリーム計算 |
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| Research Abstract |
We have obtained a new result about proof complexity of the pigeonhole principle by analyzing the space complexity and the communication complexity of findig a duplicate in a stream. Our new proof method is interesting in its own. For circuit complexity, which is closely related to proof complexity, we have (1) extended a noise-tolerant learning algorithm for AC0 functions, (2) have identified a concrete barrier for provindg a circuit-size lower bound bigger than 5n, and (3) have shown that, for n a power of 2, a smallest DeMorgan formula computing Parity of n Boolean variables is essentially unique.
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