Questions tagged [real-numbers]
56 questions
16
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2 answers
Representing Negative and Complex Numbers Using Lambda Calculus
Most tutorials on Lambda Calculus provide example where Positive Integers and Booleans can be represented by Functions. What about -1 and i?
zcaudate
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15
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2 answers
Are there established complexity classes with real numbers?
A student recently asked me to check an NP-hardness proof for them. They performed a reduction along the lines of:
I reduce this problem $P'$ that is known to be NP-complete to my problem $P$ (with a poly-time many-one reduction), so $P$ is…
Raphael
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15
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7 answers
How can a computer deal with real numbers
Computers are an exceptionally powerful tool for various computations, but they don't excel at storing decimal numbers. However, people have managed to overcome these issues: not storing the number in a decimal format, which is limited to very few…
Robert
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11
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2 answers
Decidable properties of computable reals
Is "Rice's theorem for the computable reals" -- that is, no nontrivial property of the number represented by a given computable real is decidable -- true?
Does this correspond in some direct way to the connectedness of the reals?
Shachaf
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11
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Is a function looking for subsequences of digits of $\pi$ computable?
How can it be decidable whether $\pi$ has some sequence of digits? inspired me to ask whether the following innocent-looking variation is computable:
$$f(n) = \begin{cases}
1 & \text{if \(\bar n\) occurs in the decimal representation of \(\pi\)}…
Gilles 'SO- stop being evil'
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10
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8 answers
Represent a real number without loss of precision
Current floating point (ANSI C float, double) allow to represent an approximation of a real number.
Is there any way to represent real numbers without errors?
Here's an idea I had, which is anything but perfect.
For example, 1/3 is…
incud
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Does there exist any work on creating a Real Number/Probability Theory Framework in COQ?
COQ is an interactive theorem prover that uses the calculus of inductive constructions, i.e. it relies heavily on inductive types. Using those, discrete structures like natural numbers, rational numbers, graphs, grammars, semantics etc. are very…
HdM
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7
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Unreachable Real Numbers - Randomness & Computability
I've recently read that there were many real numbers that would never be reachable by humanity. The explanation itself says that we can write as many programs as integers which is infinite, but there are infinite real numbers between two integers so…
nmomn
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Computability of equality to zero for a simple language
Suppose we have a tree in which leaves are labeled with a set of numbers $L$, and internal nodes with a set of operations $O$.
In particular $L$ can be $\mathbb{N}, \mathbb{Z}$ or $\mathbb{Q}$, and can optionally contain $\pi$ and/or $e$.
$O$ can be…
miniBill
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7
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What is the fastest algorithm to approximate an irrational number with specified precision?
Problem Background:
Let $a\in(0,1)$ to be an irrational number. Suppose there is a black box, the input is a real number in $[0,1]\backslash \{a\}$, denoted as $x$, the black box outputs boolean values according to the following rules:
When $x>a$,…
Lancdorr
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6
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1 answer
Do "Type-2" Turing machines with infinite length inputs have more computational power?
Certain idealizations of a Turing machine yield an increase in computational power, such as an inductive Turing machine, which can (trivially) solve the halting problem if it has an infinite amount of time to run.
A related variation is the "type-2…
Mike Battaglia
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5
votes
1 answer
Can a probabilistic Turing Machine compute an uncomputable number?
Can a probabilistic Turing Machine compute an uncomputable number?
My question probably does not make sense, but, that being the case, is
there a reasonably simple formal explanation for it. I should add that
I am pretty much ignorant of…
babou
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5
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Minimal positive difference of a mulitset of real numbers
Motivated by Max-Flow: Detect if a given edge is found in some Min-Cut, I'd like to ask the following questions:
Given a multiset of real numbers $B$, how hard is it to compute the minimal positive difference…
frafl
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5
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Rearrange a sequence of real numbers to satisfy polynomial inequalities
Assume we fix a degree $d$ polynomials $f$ of $k$ variables. (If it helps, let $t$ be the number of terms in $f$).
Consider a list of real numbers $a_1,\ldots,a_n$, does there exist a permutation $\pi$, such that for all $i\leq n-k$
$$…
Chao Xu
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4
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Real RAMs with "reasonable" operations
There is a large body of literature on RAMs with "reasonable" and "unreasonable" operations, where "unreasonable" operations would yield a machine with too much power to be practically feasible.
For example, it is known that for integer RAMs,…
Mike Battaglia
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