Problem Detail: I can’t figure out how to swap boxes on a Turing Machine tape. So for example, I have a tape that says a 1 0 1 1 1 0 ^ And I want to move that a over so Read More …
Category: Uncategorized
[Solved]: Real life description for (~A->A)->A
Problem Detail: It can be shown that the logical preposition [ :- (~A->A)->A ] is a theorem (always true). I want to know if anybody knows a real life description for the preposition above? I mean an expression in computer, economics, Read More …
[Solved]: What is the complexity of depth first traversal that don’t label nodes as discovered?
Problem Detail: I’ve found an algorithm that acts like a depth first traversal that don’t recognizes nodes that have been visited before. A / B C / D | E If run on this graph, the algorithm will traverse in this Read More …
[Solved]: Lexing and parsing a language with juxtaposition as an operator
Problem Detail: Normal human math notation treats juxtaposition as implied multiplication, e.g., $2x$ means $2$ multiplied by $x$. This does not seem to be a common feature of computer languages, although it was, for example, supposed to be included in the Read More …
[Solved]: What’s the time complexity of Monte Carlo Tree Search?
Problem Detail: I’m trying to find the time complexity of Monte Carlo Tree Search (MCTS). Googling doesn’t help, so I’m trying to see how far I get calculating it myself. It does four steps for n iterations, or before the time Read More …
[Solved]: If $log xy=log x+log y$ then why multiplication is harder than addition?
Problem Detail: Someone told me that the $log$ function was introduced to make the calculation easier. If we have to calculate $xy$, we can calculate instead $log x+log y$ since $log xy=log x+log y$. How this can make the calculation easier? Read More …
[Solved]: How to evaluate all derivatives of a polynomial at a point with FFT?
Problem Detail: I found this problem: Evaluating all derivatives of a polynomial at a point Given a polynomial A(x) of degree-bound n, its tth derivative is defined by From the coefficient representation $(a_0, a_1, . . . , a_{n-1})$ of A(x) Read More …
[Solved]: Combinatory interpretation of lambda calculus
Problem Detail: According to Peter Selinger, The Lambda Calculus is Algebraic (PDF). Early in this article he says: The combinatory interpretation of the lambda calculus is known to be imperfect, because it does not satisfy the $ξ$-rule: under the interpretation, $M Read More …
[Solved]: Why is the PageRank vector also the eigenvector of the web adjacency matrix?
Problem Detail: From wikipedia: The PageRank values are the entries of the dominant eigenvector of the modified adjacency matrix. This makes PageRank a particularly elegant metric Can anyone please elaborate on the connection between the eigenvector and the PR vector? Why Read More …
[Solved]: Non-termination of types in Martin-Löf’s Type:Type?
Problem Detail: In the pre-history of dependent type theory, Per Martin Löf introduced a calculus that is in some sense the simplest dependent type theory and the most general form of impredicative polymorphism. It is often referred to as Type:Type because Read More …
