All questions with tag [math: computer-science]


Turing reduction

I'm finding out algorithm concept. Research inquiry is: Are $A$ and also $B$ feasible to make sure that $A\not\le_{tt}B$ (difficult to lower making use of tt), yet $A\le_T B$. Yet I can not consider any kind of instance.
2022-07-25 20:47:10

Need little hint to prove a theorem .

I have an iterative method \begin{eqnarray} X_{k+1}=(1+\beta)X_k-\beta X_k A X_k~~~~~~~~~~~~~~~~~ k = 0,1,\ldots \end{eqnarray} with initial approximation $X_0 = \beta A^*$ ($\beta$ is scalar lying between 0 to 1)converging to the moore-penrose inverse $X =A^+$. $\{X_{k}\}$ are sequence of approximations. Assume that after $sth$ iteration...
2022-07-25 20:46:47

An algorithm to convert float number to binary representation

I need to know the algorithm of transforming an offered float (e.g, 3.14) to binary in the memory. I read this , yet it just states concerning the conversion the various other means. Allow me promptly offer the information, from the : As you recognize ; the drifting number is computed as: $value = (-1)^ {sign} \times 2^{exponent-127} \t...
2022-07-25 20:43:18

How to multiply two polynomials represented by values at distinct points?

I have two polynomials of degree $d$. However, I do not have equations for them. I simply have $d + 1$ distinct points on each polynomial. How would I find the product of these polynomials without deriving an equation for them/finding their coefficients? I would want the product of these polynomials to be represented through $2d+1$ distinct poin...
2022-07-25 20:17:03

Big O Notation reliability?

Is Big - O symbols constantly trusted? For example: Algorithm A: $n * 10^{100} = \mathcal{O}\left(n\right)$ Algorithm B: $n^{1.001} = \mathcal{O}\left(n^{1.001}\right)$ According to Big - $\mathcal{O}$ symbols, Algorithm $A$ would certainly be extra reliable, yet for all sensible objectives Algorithm $B$ is extra reliable. In a scenario simi...
2022-07-25 20:13:11

non-complete problem collapsing to a lower complexity class complete problem

Let us say that there is a NP problem that is not a complete problem. And let us assume that someone found that the problem is in fact P-complete problem. Does this imply P=NP?
2022-07-25 16:20:57

Time to resolve a problem of size $1000$ in one second, how time take resolve the same problem of size $10.000$ in $n^2$?

A algorithm call for one 2nd to settle a trouble of dimension $1000$ a neighborhood equipment. How much time time take the very same algorithm to settle the very same trouble for a trouble dimension of $10.000$ if the algorithm call for a symmetrical time to $n^2$? I assume that: T (1000) = 1 2nd, yet I do not recognize just how to develop pa...
2022-07-25 16:20:50

Master's Theorem?

When the ratio is $1$, why does the efficiency of the algorithm evaluate to $\mathcal{O} \left( n^d \log n \right)$? The total work done would be: $$T(n) = \mathcal{O}(n^d) (1+1+\cdots+1^k)$$ $$= \mathcal{O}(n^d) (1)(\log_b n)$$ where $n$ is the size of the problem, $d$ the efficiency exponent, $k$ the height of the tree and $b$ the factor the...
2022-07-25 15:57:15

Polynomial-Time reduction: Clique Problem

Here is a workout my close friend recommended to me: Show that the maximum society trouble polynomial time lowers to the maximum independent set trouble. Below is my effort at addressing it: It is recognized that the maximum independent set trouble and also the maximum society trouble are polynomially equal. Evidence of declaration: ยข - We...
2022-07-25 15:50:34

A logarithmic equation?

$$\mathcal{O} \left(3^{\log_2(n)} \right) = \mathcal{O} \left(n^{\log_2(3)} \right)$$ Does any person have any kind of suggestion just how the appropriate side was gotten to? (The $\mathcal{O}$ allows - $\mathcal{O}$ symbols)
2022-07-25 15:49:16

Form or asymptotic behaviour of $T(n) =2T(n-1)+n$

$T(n) =$ if $n=1$, then time execution is $1$, if $n \geq 2$ then $2T(n-1)+n$ The options are: $T(n) = 2^{n+1} - n - 2$ $T(n) = O(n2^n)$ $T(n) = \Omega(n)$ $T(n) = \theta(2^n)$ Thanks.
2022-07-25 15:37:59

is the language of Turing machine encodings context-sensitive?

Say we have an encoding of the set of all Turing machines/Turing programs - - WLOG, allow is claim the encoding takes values in the binary characters. Call this set of binary characters that stand for Turing Machines TM. TM will certainly be decidable as a part of all the binary characters, B, and also the getting of B obtains us a reliable lis...
2022-07-25 15:33:37

Visibility and Kernel of Polygon

I have an exercise to a give very rigorous prove to two observations of computation geometry. Obviously there are related. I've tried to prove them and wrote few ideas. Please take a look at them, and fell free to share with us your opinion. Basic theory for problem 1: A $q$ is a visible point in polygon $P$, if for every point $p \in P$, the se...
2022-07-25 15:33:19

How to find best combinations of numbers to make the sums as close as possible.

Say I am offered 8 numbers: 10, 8, 8, 7, 6.5, 5, 4 I am informed to separate the team of numbers in to 2 various teams, 4 numbers each. What formula or method is there for running every feasible mix of numbers feasible, and also ultimately result 2 teams that is numbers' amount is also or as close as feasible. I am seeking an algorithm for an ...
2022-07-24 06:47:12

Why is this Parsing Expression Grammar left recursive?

I'm trying to get my parser generator to accept this specification. I know that's kind of a programming question, but I figured this was the best place to ask. It's specified as a Parsing Expression Grammar, I think. start = Expr Expr = [0-9]+ / Sum / Product / '(' Expr ')' Product = Expr '*' Expr Sum = Expr '+' Expr Note: I know noth...
2022-07-24 06:07:56

A "State Hierarchy" Theorem for Turing Machines?

In intricacy concept, there are time power structure theories for Turing equipments that show that for sure features $f$, there exist troubles that can not be addressed by a Turing equipment in $o(f(n))$ time. Exists something equal for the variety of states in a Turing equipment? That is, exist languages for approximate $k$ that can not be det...
2022-07-22 18:32:35

"Phase change" of a purely mathematical system

Every so usually I listen to individuals speaking about "phase transitions" in totally mathematical or computer system - scientific research contexts, where there is no physics visible. Today, as an example, I listened to some individuals speaking about "phase transitions" when tinting sides in arbitrary charts. Is this simp...
2022-07-22 15:48:29

What am I describing - discrete continuity?

What area of math best describes continuous, but discrete changes in an object? For example. Example. If the start vector $(1,1,1)$ changed from itself to $(1,4,2)$ in one step, then since the 2nd component jumped up by 3, that change is not continuous, where as if it went to $(1,0,2)$ it is continuous. Now imagine if there was some final ve...
2022-07-22 15:43:49

Relationship between XOR and "AND"

I intend to XOR the password (0x3d), byte by byte, with 0x42, after that 0x51, after that 0xF7, after that 0x6F. this would certainly offer me 0xb6. Yet, Is there a faster way to this procedure?
2022-07-22 15:42:12

Longest cycle containing two nodes

We are offered a routed unweighted chart $G = (V, E)$, with $|V| \leq 100$. The objective of this trouble is to locate the lengthiest cycle having both nodes $a$ and also $b$. Just the size of that cycle is called for, not the real cycle. Many thanks a whole lot beforehand for any kind of suggestions and also pointers.
2022-07-22 15:40:48