Questions tagged [fixed-point]
29 questions
13
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2 answers
Why is least fixed point (lfp) important in program analysis
I am trying to get a big picture on the importance of least fixed point (lfp) in program analysis. For instance abstract interpretation seems to use the existence of lfp. Many research papers on program analysis also focus heavily on finding least…
Ram
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7
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How to prove that the Church encoding, forall r. (F r -> r) -> r, gives an initial algebra of the functor F?
The well-known Church encoding of natural numbers can be generalized to use an arbitrary (covariant) functor F. The result is the type, call it C, defined by
data C = Cfix { run :: forall r. (F r -> r) -> r }
Here and below, for simplicity, we…
winitzki
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6
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1 answer
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 second-order logic able to describe languages (of…
User7819
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6
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2 answers
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
further iterations make no difference. It means that…
zero_coding
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6
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1 answer
Bisimulation and the Knaster–Tarski theorem: What does the least fixed point mean?
Given a suitable lattice and a monotonic function $F$, we can compute the bisimilarity of a labeled transition system (its greatest bisimulation) by computing the greatest fixed point of $F$ using Knaster–Tarski. I was wondering if the least fixed…
Karla
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5
votes
1 answer
Self referential hash function possible?
Is there a hashing function $f$ that for each input $x$ if $f(x) = y$, then $f(x \, || \, y) = y$? In other words, if we concatenate its output with the input, the result will not change.
Furthermore, is there a simple construction for such…
prog
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5
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1 answer
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 for curiosity’s sake, have any fixed points of…
Xophmeister
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4
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2 answers
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)
public class Quine {
public static void main(String[] args) {
char quote = 34;
String[] code =…
Nathan Wood
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3
votes
1 answer
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 complete without a quine.
I give a slightly…
Christopher King
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3
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2 answers
Notation for a Kleene fixed point with a starting element
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 composed with itself) leads to a fixed point of…
choeger
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3
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2 answers
Is there any research on "fixed points of bugs"?
Is there any research on or at least formulation of the concept of "fixed points of bugs"? That is, suppose we have an implementation $I$ (e.g., a compiler or interpreter) of a programming language $L$. There is some bug $B$ (we define a bug as…
Shiho Miyano
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3
votes
1 answer
How is the input to a BROUWER algorithm done
The Brouwer fixpoint theorem states that any continuous mapping $f$, from a convex, compact set to itself will contain a fixpoint.
The Brouwer algorithm finds these (approximate) fixpoints. But how is a continuous function inputted into this…
Andrew Baker
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3
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1 answer
What are the fixed-points of the Y combinator?
Since the Y combinator itself is a function (albeit a higher-order one), I was wondering what the fixed-points of Y itself are.
brj
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1
vote
2 answers
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 please explain me what's the essence of dividing by this? Why does this dividing works…
ntrsBIG
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1
vote
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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 I build a matrix M:
U = [v1 v2 v3]
So I…
f.saint
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