Problem Detail: The Existential Theory of the Reals is in PSPACE, but I don’t know whether it is PSPACE-Complete. If I believe that it is not the case, how could I prove it? More generally, given a problem in some complexity Read More …
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[Solved]: Relation between the “Point-Cover-Interval” problem and the “Interval Scheduling” problem
Problem Detail: Point-Cover-Interval Problem: Given a set $mathcal{I}$ of $n$ intervals $[s_1, f_1], ldots, [s_n, f_n]$ along a real line, find a minimum number of points $P$ such that each interval contains some point, that is $forall I in mathcal{I}: Read More …
[Solved]: Can a transcendental number like $e$ or $pi$ be compressed as not algorithmically random?
Problem Detail: The related and interesting fields of Information Theory, Turing Computability, Kolmogorov Complexity and Algorithmic Information Theory, give definitions of algorithmically random numbers. An algorithmically random number is a number (in some encoding, usually binary) for which the shortest program Read More …
[Solved]: Pseudo polynominal time algorithm for Np-Complete Problems
Problem Detail: For problems like knapsack there is pseudopolynominaltime algorithm and it is np-complete. So we reduce every other problem in np in polytime to knapsack. But why don’t we have then a pseudopolynominaltime algorithm for all problems in np? Asked Read More …
[Solved]: Is the language of TMs that decide some language Turing-recognizable?
Problem Detail: Is the language $qquad L={ langle text{M} rangle ; | ; text{M is a Turing machine that decides some language} }$ a Turing-recognizable language? I think it’s not, as, even if I am able to tell somehow that a Read More …
[Solved]: Proof that ${⟨M⟩ ∣ L(M) mbox{ is context-free} }$ is not (co-)recursively enumerable
Problem Detail: I would like to use your help with the following problem: $L={⟨M⟩ ∣ L(M) mbox{ is context-free} }$. Show that $L notin RE cup CoRE$. I know that to prove $Lnotin RE$, it is enough to find a language Read More …
[Solved]: Order a list of whole numbers so that no two numbers have the average of them sitting between them
Problem Detail: Given a whole number N.. Arrange 1 to N in a sequence such that no two numbers have their average sitting between them… Note – If N=20.. average of 19 and 2 = 10.5 is not a whole number Read More …
[Solved]: Can we check in polynomial time if the language of a DFA is closed against Kleene star?
Problem Detail: I was wondering if there is a polynomial time algorithm to test whether a DFA recognizes a star closed language ( which is if $A=A^*$). I think that yes, but I do not have an idea to do it. Read More …
[Solved]: How does insertion work in an AVL tree?
Problem Detail: From the above image, while trying to maintain an AVL tree data structure, how would the tree look after inserting the value 10? Also, if anyone has any suggestions or simple method of rotating, feel free to share. Read More …
[Solved]: Is the image of a function the codomain of a function?
Problem Detail: Here is a definition from the functions section in my discrete math textbook (Discrete Mathematics and its Applications 7e, Rosen 2012): Let $f$ be a function from $A$ to $B$, and let $S$ be a subset of $A$. The Read More …
