1
vote
3answers
90 views

Recurrence relations (Big-O notation)

Say I'm given a recursive function such as: function(n) { if (n <= 1) return; int i; for(i = 0; i < n; i++) { function(0.8n) } } ...
0
votes
0answers
21 views

Expressing three recursive forms into one using parameters?

I have the following recursive function that takes three forms and I want to express it in one form: Initial: $f(x) = m * f(x-1)$, $f(0) = value.$ Forms: 1 - $f(t) = m * f(t-1)$. where t is at ...
1
vote
1answer
57 views

On the size of a set of functions such that $f(i)\ne f(i+1)$ for every $i$ (and similar conditions)

For a finite set $A$,let $|A|$ denote the number of elements in the set $A$. (a) Let $F$ be the set of all functions $$f: \{1,2,\ldots,n \} \to \{1,2,\ldots,k\}~~~~~~~~~~ (n\ge 3,k\ge 2)$$satisfying ...
3
votes
1answer
50 views

Structure of partial recursive function over recursively enumerable guard

I read that the function $$ f(n) = \left\{ \begin{array}{l l} g(n) & \quad \text{if $n \in A$}\\ \text{undefined} & \quad \text{otherwise} \end{array} \right. $$ is recursive if ...
4
votes
3answers
57 views

Recursion, multiplication and exponential

The set $F_{n}$ of primitive recursive function symbols of arty $n$ can be defined inductively as \begin{array}[lr] & Z, \text{Succ} \in F_{1} & \\ \pi_{j}^{n} \in F_{n} \quad \text{for each} ...
0
votes
1answer
43 views

Recursive function

Having difficulty with a question, was hoping someone could take a look and explain (if) where i'm going wrong. Consider the following recursive definition of a function $f:N\to N$ Base case: For ...
0
votes
1answer
25 views

Defining a recursive function $f$ on $\{a, b\}$*

I would need some help on how I can define a recursive function $f$ on $\{a, b\}$* Define a recursive function $f$ on $\{a, b\}$* which replaces any $a$ with $b$ and vice versa, for example, ...
0
votes
2answers
57 views

I need some help on solving a recursive function question

I'm working on a recursive function task which i'm a bit stuck at. I've tried to google it on how I can solve this task, but with no luck Here is the task: Provide a recursive function $r$ on ...
0
votes
1answer
67 views

How can I solve this recursion function task?

I really need help on this task. Im stuck at it and I really would appreciate your help here. Give a recursive function $r$ on $A$ that reverses a string. For instance, $r(logikk) = kkigol$ and ...
0
votes
0answers
42 views

Find the characteristic equation of a recursive function

I want to determine whether the following recursive function is unstable; $$ x(t+1) = \left( wx+sx(t)^b \over w+x(t)^bs + (1-x(t))^b(d-s) \right) $$ Wikipedia is telling me that I want to have the ...
2
votes
0answers
96 views

Repertoire method for solving recursions

I am trying to solve this four parameter recurrence from exercise 1.16 in Concrete Mathematics: $g(1) = \alpha;$ $g(2n+j) = 3g(n) + γn + β_j$ : j = 0,1 and n >= 1 I have assumed the closed form to ...
0
votes
1answer
115 views

Computing functions from generating functions

I am new to generating functions but understand how to derive them from given discrete numeric functions. Is there a simple way to derive the discrete numeric function given a generating function. For ...
1
vote
1answer
158 views

Representing Recursion and Primitive Recursion diagrammatically

I'm interested in how Recursion, and Primitive Recursion, could be represented diagrammatically. It occurred to me that this would be a good way of seeing the difference. Also, I'm interested in how ...
1
vote
3answers
134 views

Mathmatical representation of recursion function

Well i'm not so good at math, but i have the following task: Here's the code: ...