Tsuyoshi Ito
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 Sep1 comment Techniques for summing ratio of binomial coefficients I cannot move your question because I am not a moderator. Sep1 comment Techniques for summing ratio of binomial coefficients At least for me, this question is fairly uninteresting because it looks like just a random formula, and I fail to see why it is reasonable to expect that it has a nice closed-form expression (and also because I am not good at this kind of math). If you state why you are interested in this sum, some people may care more. Sep1 comment Techniques for summing ratio of binomial coefficients Moderators are not checking all comments to all questions. If you have a question to moderators, it is more reliable to flag your own question, choose “it needs ♦ moderator attention,” and explains why it needs moderator attention. Jul11 comment NP-completeness and NP problems @TonyK: If P=NP, why does switching from RSA to elliptic curve cryptosystems help? Jun13 comment Solving P vs NP with computer As you stated in the comments, you have made a few important assumptions to connect your answer to the question being asked. Instead of explaining those assumptions to me, why don’t you just state them in your answer? Making important assumptions implicitly is a bad way to talk about theory. Jun13 comment Solving P vs NP with computer @Quinn Culver: And what I meant is that undecidability of P=NP in a certain theory (whether neither P=NP nor P≠NP is provable in that particular theory) has nothing to do with the undecidability which Kaveh is talking about. Jun13 comment Solving P vs NP with computer @Quinn Culver: I am afraid that you are mixing up the decidability in the computability theory and the decidability (in a specific theory) in the formal logic theory. A single question (such as "is P=NP provable in ZFC?") cannot be undecidable in the computability sense. Jun13 comment Solving P vs NP with computer You generalized the question, pointed out that the generalized question is undecidable, and apparently concluded that the original question is hard. This is analogous to saying “solving the Hamiltonian circuit problem on the Petersen graph is hard because the Hamiltonian circuit problem is NP-complete.” May12 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. Mar27 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. Mar16 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. Mar11 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. Mar10 comment P or NP-Complete? (concerning 2-CNF formulas) @J.D.: cs.stackexchange.com is currently in private beta. Feb24 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. Feb19 comment The Average Running Time Of Euclid Algorithm? What do you mean by “define it in the limit”? Feb19 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. Feb16 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. Feb16 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. Feb16 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. Feb15 comment The Average Running Time Of Euclid Algorithm? For every d, there are infinitely many pairs (m,n) such that gcd(m,n)=d. How do you define the average?