Tsuyoshi Ito
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 May 12 comment non-complete problem collapsing to a lower complexity class complete problem In the last paragraph, if P=NP, then it does mean that every P-complete problem under log-space reducibility is NP-complete under polynomial-time reducibility. I think that you meant to write the opposite: even if P=NP, it does not mean that every NP-complete problem under polynomial-time reducibility is P-complete under log-space reducibility. Apr 7 revised How to simpify the way of calculating $(a^b \bmod c) \bmod d$? wording; tex Apr 7 suggested approved edit on How to simpify the way of calculating $(a^b \bmod c) \bmod d$? Apr 7 revised How to simpify the way of calculating $(a^b \bmod c) \bmod d$? wording; tex Apr 7 suggested approved edit on How to simpify the way of calculating $(a^b \bmod c) \bmod d$? Apr 2 awarded Tag Editor Apr 2 revised graph-theory wiki description linked to tag:graph to explain that it is different from this tag Apr 2 suggested approved edit on graph-theory tag wiki Mar 27 comment How is the graph coloring problem NP-Complete? You are talking about coloring of a planar graph, but strictly speaking, the question is about coloring of a general graph. Mar 16 comment A non-distinct system of representative edges. @utdiscant: I prefer your terminology, but some people prefer to treat an edge of a graph as a set of two vertices, in which case the wording of the question is fine. Mar 11 comment Knapsack with non-trivial “utility” function In the standard Knapsack problem, only single copy of each item is available. You are probably talking about a variation of the NP-hard problem called the unbounded Knapsack problem. Please check the Wikipedia article which you linked to. Mar 10 comment P or NP-Complete? (concerning 2-CNF formulas) @J.D.: cs.stackexchange.com is currently in private beta. Feb 29 awarded Enlightened Feb 29 awarded Nice Answer Feb 24 comment Properties of a valid DFA @CamMcLeman: The word “equivalent” in your comment has to be interpreted with caution, because people care about the difference between, say, DFA and NFA, although they are fairly easily proven “equivalent” under some standard terminology. Feb 19 comment The Average Running Time Of Euclid Algorithm? What do you mean by “define it in the limit”? Feb 19 comment No identical rectangles in a matrix There is an $O(N^2 M \log M)$-time algorithm. (Hint: First consider the case of a 2×M matrix.) I do not know if there is a faster one. Feb 16 comment 1/3+2/3 in double precision In general, if you cannot be sure of the correctness of your own calculation, one of the good ways to check the correctness is by writing down steps more carefully. In your case, the first step is to represent 1/3 and 2/3 as double-precision floating-point numbers. Feb 16 comment How can I create/modify 3-SAT functions according to Valiant-Varizani? (1) If you do not understand the proof, then do not say “it’s fairly straightforward.” It may seem cool to say that, but it gives a wrong impression that you believe that you have understood the proof. (2) First, forget Boolean formulas (let alone 3CNF formulas) and understand the algorithm which computes h(x) in the lecture note. It is straightforward, but you cannot go forward without understanding that part. After that, convert the algorithm to a 3CNF formula, either by making some observations about the algorithm or by using the reduction in the Cook-Levin theorem. Feb 16 comment How can I create/modify 3-SAT functions according to Valiant-Varizani? Judging from the last paragraph, I doubt that you understand the proof of Valiant-Vazirani, in particular the use of pairwise independent family of hash functions in the proof.