# Tagged Questions

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### operator vs operation vs function vs procedure vs algorithm

I have a vague understanding of what operator, operation, function, procedure, algorithm mean in general. I am heavily biased towards computer science. Do you agree with them? What are the generally ...
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### Seam Carving - Energy functions. How do they work?

I have been taking an interesting in dynamic programming and more specifically Seam Carving. For those who are not aware what this is, please look here and for some more detailed information here. If ...
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### Getting a diverse set of three numbers from two numbers

I'm using this information to build an interface to pick a color, but I feel that this question is purely math-related. Please correct me if this is the wrong StackExchange site for this. I am making ...
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### Why is there information loss here?

I posted this a while ago, but realized that actually this works, but produces information loss. Here is the process: Let's try to reduce a number $x$. We will be using base $\beta$ for this process. ...
56 views

### Function Combination on Computer Science

I read some material on Computational Function, every one could describe the result of following combination? suppose $g_1(x)=3x$, $g_2(x)=4x$, $f(x,y)=x+y$, how we compute combination of $f$ with ...
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### Subscript before a function symbol?

Does anyone know what the subscript before the function means? $$_pf_p$$ It's part of a definition for selfish routing in networks: Let $N = (V,E)$ be the network, which is a directed graph. ...
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### Are all constrtuctively describable functions continuous? Do they necessarily come with a topology?

In the paper "An injection from $\mathbb{N}^\mathbb{N}$ to $\mathbb{N}$" by @AndrejBauer, about the question whether there exists an injection $\mathbb{N}^\mathbb{N}\to\mathbb{N}$, we writes ...
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### How to prove such program is uncomputable

We say that two programs are equivalent if they give the same output on every input. Prove that it is impossible to write a computer program that takes as input two pieces of code, code1 and code2, ...
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### How can I tell/compare the asymptotic complexity of a function?

For something, like a quadratic I just take the highest degree and see if it is theta or big O or Omega of n, correct? So like 2n^2+2n+1 could be theta(n^2). What are the general ...
349 views

### Ceiling to Floor Function Conversion Proof

I am working on a proof to convert a ceiling of a fraction to a floor of a fraction. I found this: \begin{aligned} q=\left\lceil \frac{n}{m} \right\rceil \;&\Leftrightarrow\; \frac{n}{m} \leq q ...
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### What's the term for a value x that satisfies the constraint $f(x) = f$ for a function f?

I know that $x$ is called the fixed point of a function $f$ if it satisfies the constraint $f(x) = x$. However, for a function $f$ if there exists some value $x$ such that $f(x) = f$ then what is the ...
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### Upper bound for linear function

What may be more surprising is that when $a>0$, any linear function $an +b$ is $\mathcal{O}(n^2)$ which is easily verified by taking $c = a + |b|$ and $n_o = \max (\frac{-b}{a}, 1)$. an + b ...
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### How to show if a function is partial recursive?

I have seen and understood the most definitions but i just could not understand how to show if a function is mu-partial recursive or not. I used search engines, but all I find are just more lectures ...
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### Converting an IF condition to a mathematical equation

I am trying to study about converting algorithms into mathematical equations. For this I just started with a simple random example : ...
428 views

### How do I turn this piecewise function into a “normal” function?

I am a Java developer building a web app that I will be deploying "in the cloud" (I hate that expression) in a few months. I'm trying to develop a function that will let me spawn and kill the right ...
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### Terminology for a function computed by a finite-state transducer?

A finite-state transducer is a generalization of a finite state machine that accepts an input string and produces an output string (instead of just accepting or rejecting). Is there a name for a ...
210 views

### Alternate expression for the following function

So if the following function is evaluated with the floating-point arithmetic, we get poor results for certain range of values of $x$. Therefore, I need to provide an alternate function that can be ...
656 views

### calculating unique value from given numbers

let's say I have some (n) random numbers 12, 13, and 18. I want to calculate some unique value from these three such that if I change their order 13, 12, 18 or 18, 12, 13..whatever order they are in, ...
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### Some problem with function, operator, and optimization.

Actually, this problem come from a programming language challenge. The objective is: to create a one-to-one function, $f$, that mapped A into B with A = {0, 1, 2, 3, 4, 5, 6}, and B = {1, 5, 10, 50, ...
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### Perfect Hash Function just an Injection?

I just read up on the concept of perfect hash functions on a set $S$. I am quoting: "A perfect hash function for a set S is a hash function that maps distinct elements in S to a set of integers, with ...
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### non time constructible functions

A function $T: \mathbb N \rightarrow \mathbb N$ is time constructible if $T(n) \geq n$ and there is a $TM$ $M$ that computes the function $x \mapsto \llcorner T(\vert x\vert) \lrcorner$ in ...
I need to avoid using an if statement that does a $\geq$ comparison, (I'm writing HLSL code for the xbox). I need a function such that $f(x, y) = 0$ when $x < y$ and $f(x,y)=1$ when $x \geq y$. ...
It seems obvious to me that the set of functions with the signature $\forall A. A \rightarrow A$ is "once-inhabited", i.e. there is only one such polymorphic function which "works" for any set $A$, ...