Satisfiability Algorithm for Syntactic Read-kk-times Branching Programs

The satisfiability of a given branching program is to determine whether there exists a consistent path from the root to 1-sink. In a syntactic read-k-times branching program, each variable appears at most k times in any path from the root to a sink. We provide a satisfiability algorithm for syntactic read-k-times branching programs with n variables and m edges that runs in time Oleft(poly(n, m^{k^2})cdot 2^{(1-mu(k))n}right), where mu(k) = frac{1}{4^{k+1}}. Our algorithm is based on the decomposition technique shown by Borodin, Razborov and Smolensky [Computational Complexity, 1993]

A Much Faster Algorithm for Finding a Maximum Clique

We present improvements to a branch-and-bound maximumclique-finding algorithm MCS (WALCOM 2010, LNCS 5942, pp. 191–203) that was shown to be fast. First, we employ an efficient approximation algorithm for finding a maximum clique. Second, we make use of appropriate sorting of vertices only near the root of the search tree. Third, we employ a lightened approximate coloring mainly near the leaves of the search tree. A new algorithm obtained from MCS with the above improvements is named MCT. It is shown that MCT is much faster than MCS by extensive computational experiments. In particular, MCT is shown to be faster than MCS for gen400 p0.9 75 and gen400 p0.9 65 by over 328,000 and 77,000 times, respectively

Card-Based ZKP Protocols for Takuzu and Juosan

International audienc

木構造関数値評価問題と分岐プログラム充足性問題に対する計算複雑さ

京都大学0048新制・課程博士博士(情報学)甲第19129号情博第575号新制||情||101(附属図書館)32080京都大学大学院情報学研究科通信情報システム専攻(主査)教授 岩間 一雄, 教授 髙木 直史, 教授 五十嵐 淳学位規則第4条第1項該当Doctor of InformaticsKyoto UniversityDFA