computable

USAGE SUMMARY

The phrase "computable" is correct and usable in written English. You can use it in contexts related to mathematics, computer science, or logic, where it refers to something that can be calculated or determined by a computational process. For example: "The function is computable within a finite amount of time." Alternative expressions include "calculable" and "determinable."

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

57 human-written examples

Turing also showed that there are universal Turing machines — machines that can compute any function computable by any other Turing machine.

SEP

In addition, there is an extensive classification of computable problems into computational complexity classes according to how much computation as a function of the size of the problem instance—is needed to answer that instance.

SEP

By adopting a convention for representing TRUE and FALSE, perhaps that TRUE is represented as a sequence of two '1's and FALSE as one '1', we can design Turing-machines to compute the characteristic functions of computable predicates.

SEP

Blum et al.'s result is equivalent to demonstrating that all functions over denumerable domains — including the uncountably many functions that are not Turing-computable — are computable by Blum et al.'s "computing" systems, which are allowed to manipulate the exact values of arbitrary real numbers.

SEP

He proved that no Turing machine can compute the values of the function D that I described earlier, and he argued that his model of human computation is sufficiently general, in the sense that there are no intuitively computable (i.e. effectively calculable) functions that Turing machines are incapable of computing.

SEP

It gave a fresh approach to the traditional mind-body problem, by relating it to the mathematical concept of computability he himself had introduced in his 1936 7 paper "On computable numbers, with an application to the Entscheidungsproblem".

SEP

A mathematical problem is computable if it can be solved in principle by a computing device.

SEP

Part of the reason lies in the computable general equilibrium (CGE) models used by the Bank's (and other) economists.

The Economist

Human-verified similar examples from authoritative sources

Similar Expressions

3 human-written examples

It only says that if something physical is a computing system, then the functions it computes are Turing-computable.

SEP

Quantum hypercomputation is rarely discussed in the literature (See, e.g., Calude et al. 2003), but the most concrete attempt to harness quantum theory to compute the non-computable is the suggestion to use the quantum adiabatic algorithm (see below) to solve Hilbert's Tenth Problem (Kieu 2002, 2004)—a Turing-undecidable problem equivalent to the halting problem.

SEP

All computing mechanisms that have been physically built or are in the process of being built compute only functions that are Turing-computable.

SEP

Expert writing Tips

Best practice

When writing about theoretical computer science, use "computable" to precisely denote functions or problems solvable by a Turing machine. This ensures clarity and avoids ambiguity.

Common error

Avoid using "computational" when you specifically mean a function is solvable in principle. "Computational" refers to the process of computation itself, while "computable" indicates the possibility of being computed.

Linguistic Context

The word "computable" functions primarily as an adjective, modifying nouns to describe whether something can be calculated or determined algorithmically. As Ludwig AI confirms, this term is correct and applicable in contexts relating to computation and mathematics.

Expression frequency: Uncommon

Frequent in

Science

78%

News & Media

22%

Formal & Business

0%

Less common in

Academia

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, "computable" is a term used to describe whether a problem or function can be solved algorithmically, particularly by a Turing machine. As Ludwig AI indicates, it is grammatically correct and suitable for technical and academic contexts. While primarily found in scientific discourse, it occasionally appears in news media. When writing, be sure to distinguish it from similar terms like "computational" and consider alternatives like "calculable" or "solvable" depending on the nuance you intend to convey. The most frequent and authoritative source is Stanford Encyclopedia of Philosophy.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

calculable

Indicates the possibility of calculating a value or result, focusing on the process of calculation.

solvable algorithmically

Emphasizes that a solution can be found through an algorithm, highlighting the algorithmic nature of the solution.

determinable

Focuses on the ability to ascertain or establish something definitively, regardless of the method.

decidable

Implies that a definite answer (yes or no) can be obtained for a given problem, relevant in logic and computer science.

machine-executable

Highlights the capability of a set of instructions to be run by a machine, particularly in programming.

algorithmically decidable

Combines the concepts of algorithms and decidability, indicating a problem that can be resolved by an algorithm.

programmable

Indicates that something can be configured to perform a task through programming.

resolvable

Suggests that a problem or question can be settled or clarified.

amenable to computation

Expresses that a task or problem is suitable for computational methods.

computationally tractable

Indicates that a problem can be solved with reasonable computational resources, especially time and memory.

FAQs

How is "computable" used in technical writing?

In technical contexts, "computable" typically describes whether a problem or function can be solved by an algorithm, often in the context of Turing machines or other computational models.

What's the difference between "calculable" and "computable"?

"Calculable" generally means something can be determined by calculation, while "computable" specifically refers to being solvable by a computational process or algorithm, often implying Turing-computability.

When should I use "solvable" instead of "computable"?

Use "solvable" when you want to emphasize that a problem has a solution, while "computable" emphasizes that the solution can be obtained through a specific computational process.

Can "computable" apply to non-mathematical contexts?

While primarily used in mathematical and computer science contexts, "computable" can metaphorically extend to other domains where processes can be modeled algorithmically, although such usage should be considered carefully.