Problem Detail: Reading this question “Natural RE undecidable problems but not Turing-complete” the following language came to my mind: If $Sigma(cdot)$ is the busy beaver function (maximum attainable score among all halting 2-symbol n-state Turing machines of the above-described type, when Read More …
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[Solved]: Are randomized algorithms constructive?
Problem Detail: From , the proofs by the probabilistic method are often said to be non-constructive. However, a proof by probabilistic method indeed designs a randomized algorithm and uses it for proving existence. Quoted from p103 of Randomized Algorithms By Rajeev Read More …
[Solved]: Inapproximability result implies apx-hardness?
Problem Detail: If an optimization problem is known to be inapproximable up to some precision, does this automatically imply that the problem is apx-hard? Asked By : mat Answered By : Yuval Filmus If P$=$NP then there is a polytime algorithm for any Read More …
[Solved]: Is there a simple example of sets such that $A leq_T B$ but not $A leq_m B$?
Problem Detail: I wonder if there is a simple example of sets $A$ and $B$ such that $A$ is Turing-reductible to $B$ but not many-to-one reductible to $B$. Asked By : pintoch Answered By : Martin Jonáš For example sets $H = {x Read More …
[Solved]: Can a Turing machine decide if a LOOP program stops for the integer input 0
Problem Detail: This is a question I found in a practice exam while I am preparing for my mid term exam. The answer needs justification, either a pseudo code or a logical explanation why not. What puzzled me about that question Read More …
[Solved]: When testing n items, how to cover all t-subsets by as few s-subsets as possible?
Problem Detail: This problem arose from software testing. The problem is a bit difficult to explain. I will first give an example, then try to generalize the problem. There are 10 items to be tested, say A to J, and a Read More …
[Solved]: Complement of HAMPATH
Problem Detail: Is the complement of the Hamiltonian Path problem known to be in $mathsf{NP}$? I could not find explanations saying that it is, but then neither were there any claims saying that it is not in $mathsf{NP}$. Asked By : pnp Read More …
[Solved]: Greedy algorithm correctness proof for “Elegant Permuted Sum” (UVa 11158)
Problem Detail: Given a sequence of $2 leq n leq 50$ numbers $s = (s_1,s_2,…,s_n)$, find a permutation $a = (a_1,a_2,…,a_n)$ of $s$ such that $$sum_{i=1}^{n-1} |a_i – a_{i+1}|$$ is maximized. I found many codes that get “Accepted” in the online Read More …
[Solved]: How many permutations in a trainset?
Problem Detail: If I have the following pieces to a train set: (12) Curve (4) Straight Such as this train set. I’m looking for an algorithm (to which I can write a program) that creates/lists all permutations. It’s not as simple Read More …
[Solved]: Type-system combining type-states and typed effects?
Problem Detail: Has anyone succeeded in implementing or designing a type-system that combines both type-state (linear types) and effect types (e.g. Koka)? Asked By : Olle Härstedt Answered By : Matija Pretnar Edwin Brady has done some work in that area using dependent Read More …
