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Questions tagged [fixed-point]

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11
votes
2answers
2k views

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 ...
5
votes
2answers
581 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) ...
4
votes
2answers
362 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 ...
4
votes
1answer
197 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 ...
4
votes
1answer
133 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 ...
3
votes
2answers
47 views

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 ...
2
votes
1answer
62 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 ...
1
vote
1answer
1k 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 ...
1
vote
1answer
128 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 ...
1
vote
1answer
417 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 ...
1
vote
1answer
51 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: ...
1
vote
0answers
26 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 ...
0
votes
2answers
331 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 ...
0
votes
0answers
9 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 ...
0
votes
0answers
32 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: ...