# Questions tagged [fixed-point]

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### Find the fixed point of a recursive functional?

A functional is a function which takes another function as a parameter. The fixed point of a function is an input such that F(x) = x Given an example ...
35 views

### Termination of Z combinator with call-by-value

I am trying to build my own λ-calculus interpreter. So far it supports both call-by-value and normal order. I now want to try recursion via fixed points. The $Y$ combinator works with normal order, ...
11 views

### Is Decimal (correctly-rounded arbitrary precision decimal floating point arithmetic) fixed-point, floating-point or something else?

The Decimal data type I am referring to is GNU MPFR(https://en.wikipedia.org/wiki/GNU_MPFR), or libmpdec (http://www.bytereef.org/mpdecimal/doc/libmpdec/index.html). I have been searching for ...
66 views

### Fixed Points of Factorial Function

(This is taken from the book Semantics with Applications) I'm trying to determine the fixed points for the following block: ...
33 views

### Trying to determine Fixed Points

I'm basically trying to solve 4.2 (Taken from Semantics with Applications) As I see it, the functional F will be defined like so: ...
232 views

### Fixed point of hash

Are hashing algorithms constructed to guarantee that no fixed point exists? My assumption is not, because I don’t see what utility that would have. (Please correct me if I’m wrong.) As such, purely ...
227 views

### Logical characterization of P versus NP problem (and references for least fixed point logic)

Wikipedia says the following (and more) about the logical characterization of the P versus NP problem here: Thus, the question "is P a proper subset of NP" can be reformulated as "is existential ...
628 views

### Why Does the Fixed Point Theorem Apply to Quines?

A quine is a program that outputs its own source code without taking in any input. An example would be this (taken from here) ...
2k views

### How does conversion from fixed-point to floating-point happen?

I came across to the code that convert 32-bit signed fixed-point number (16.16) to a float and it looks like (pseudocode) floating = fixed / 65536.0 Could you ...
30 views

### Hebbian rule doesn't get to a fixpoint

I'm trying to implement an Hopfield Network for pictures of 32x32 bits either 1 or -1; I have these 3 pictures and I transform each of them in a vector of 1024 elements. Then I take the 3 vectors and ...
140 views

### Is Datalog negation and the built-in predicate $\neq$ similar?

I was reading "Principles of Database & Knowledge-Base Systems, Vol. 1" by Jeffrey D. Ullman. There is a chapter about Datalog negation and as I was seeing the problems of negation I kept thinking ...
443 views

### Neural Networks: Simulate the working of Dynamic Fixed Point representation of the weights on hardware

I am looking to implement a neural network on hardware using Verilog. I have completed and tested with floating point representation and a 20 bit fixed point representation. I want to further reduce ...
730 views

### What is a fixpoint?

Could someone please explain me, what is a fix point? I caught the minimum explanation about fix point from the website: After infinitely many iterations we should get to a fix point where ...
68 views

### Why doesn't this quine-less language contradict Kleene's recursion theorem?

Kleene's recursion theorem implies that every Turing complete programming language that satisfies certain properties have quines. This website claims that this is incorrect, and that there is a Turing ...
376 views

### Decimal to Fixed Point Conversion

I am having trouble to get the intuition behind the following approach: We take the fraction point (say: .642) and continuously multiply by 2, taking whatever ends up right of the point as our next ...
Assume a CPO $Q,\leq$ and a Scott-continuous function $f : Q \rightarrow Q$. As it is known, the chain $\bot \leq f(\bot) \leq \ldots \leq f^n(\bot)$ (where $f^n$ denotes the function $n-1$-times ...