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Problem Detail: I just read some pages in Sipser’s book Introduction to Theory of Computation about Post Correspondence Problem, and I’m thinking that PCP is actually in NP. The certifier is: for an input configuration of pile $$(t_1/b_1, t_2/b_2,…t_n/b_n)$$ concatenating $t_1, Read More …

Problem Detail: I’ve tried to solve a exercise 4.1-5 in algorithm book “Introduction to algorithms”. it is about Maximum sub-array problem, which is an algorithm that determines the greatest sum of sub-array A[i], A[i+1] , … , A[j] in given array Read More …

Problem Detail: I was wondering about a variation on the Stable Marriage Problem. Initially, we have two sets of entities, usually males and females, and they have preference lists ranking the other group, and through a series of proposals, we end Read More …

Problem Detail: I am learning about information theory and mutual information. However, I am quite confused with MI(Mutual information) vs. PMI(Pointwise mutual information) especially signs of MI and PMI values. Here are my questions. Is MI values a non-negative value or Read More …

Problem Detail: I have few CS textbooks with me which discuss languages, well actually 2 plus old course notes supplied a few years ago. I have been searching the web too any only seem to come up with vague responses just Read More …

Problem Detail: Given an $n times n$ matrix $mathbf{A}$. Let the inverse matrix of $mathbf{A}$ be $mathbf{A}^{-1}$ (that is, $mathbf{A}mathbf{A}^{-1} = mathbf{I}$). Assume that one element in $mathbf{A}$ is changed (let’s say $a _{ij}$ to $a’ _{ij}$). The objective is to Read More …

Problem Detail: I read somewhere that 3SAT can be used to solve Integer Factorization. If that is true, could someone teach me a simple example of generating the 3SAT by using a small number? Let’s say you are given the number Read More …

Problem Detail: Let’s say we a have flow network with $m$ edges and integer capacities. Prove that there exists a sequence of at most $m$ augmenting paths that yield the maximum flow. A good way to start thinking about this is Read More …

Problem Detail: What operations need to be performed in order to do any arbitrary analogue computation? Would addition, subtraction, multiplication and division be sufficient? Also, does anyone know exactly what problems are tractable using analogue computation, but not with digital? Asked Read More …

Problem Detail: I come across this definition but it’s not so clear for me ! An array is partially sorted if the number of inversions is less or equal a constant times the array length. if array length is N then Read More …