Computability: meaning, definitions and examples

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computability

 

[ ˌkɒmˌpjuː.təˈbɪl.ɪ.ti ]

Noun
Context #1 | Noun

theory

The quality or state of being computable; the ability to be solved by an algorithm or a computer program.

Synonyms

algorithmic solvability, computational feasibility, solvability.

Which Synonym Should You Choose?

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Word Description / Examples
computability

Discussing whether a problem can be solved using a computer through any algorithm and asking if there exists a theoretical computational method.

  • The computability of this function has been a major topic in theoretical computer science.
  • Researchers are exploring the computability limits of this complex problem.
solvability

A general term applicable in any context where the main concern is whether a problem or equation can be solved, not necessarily by a computer.

  • The solvability of the puzzle intrigued mathematicians for years.
  • He questioned the solvability of ethical dilemmas in artificial intelligence.
algorithmic solvability

Used when focusing on the existence of a specific algorithm that can solve a problem efficiently.

  • We need to determine the algorithmic solvability of this equation within polynomial time.
  • The algorithmic solvability of scheduling issues in large projects is well-documented.
computational feasibility

Concerning whether a problem can be solved within practical limits of time and resources. Typically used in engineering or applied settings.

  • Considering computational feasibility, this project might require more resources than we have.
  • The computational feasibility of real-time processing should be evaluated before implementation.

Examples of usage

  • The computability of certain mathematical problems has been a topic of research for decades.
  • Many real-world problems can be reduced to questions of computability.
Context #2 | Noun

computing

The extent to which a problem or function can be computationally solved or executed.

Synonyms

algorithmic feasibility, computational solvability, executability.

Which Synonym Should You Choose?

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Word Description / Examples
computability

Another mention as it is the same word, sometimes context-specific in different phrases or discussions within academic or technical fields.

  • The computability of complex systems is always an intriguing topic.
  • Research on computability often involves theoretical models and proofs.
executability

Refers to whether a specific program or script can be executed or run successfully on a computer, often used in practical or operational contexts.

  • The script's executability depends on having the correct runtime environment.
  • We need to test the executability of the new software module before deployment.
algorithmic feasibility

Focuses on whether a problem can be solved efficiently by an algorithm, considering practical limitations such as time and resources.

  • While the problem is computable, its algorithmic feasibility is questionable due to its exponential time complexity.
  • Algorithmic feasibility plays a crucial role in software engineering.
computational solvability

Often used interchangeably with computability, it places a slight emphasis on the ability to find a solution using computational methods.

  • The computational solvability of this equation was previously unknown.
  • Computational solvability can often be established using advanced algorithms.

Examples of usage

  • Programmers often consider computability when designing algorithms.
  • The computability of a problem can impact the efficiency of a program.

Translations

Translations of the word "computability" in other languages:

🇵🇹 computabilidade

🇮🇳 गणनीयता

🇩🇪 Berechenbarkeit

🇮🇩 komputabilitas

🇺🇦 обчислюваність

🇵🇱 obliczalność

🇯🇵 計算可能性

🇫🇷 calculabilité

🇪🇸 computabilidad

🇹🇷 hesaplanabilirlik

🇰🇷 계산 가능성

🇸🇦 قابلية الحساب

🇨🇿 počitatelnost

🇸🇰 počítačnosť

🇨🇳 可计算性

🇸🇮 računljivost

🇮🇸 útreiknanleiki

🇰🇿 есептелушілік

🇬🇪 ანგარიშსწიფობა

🇦🇿 hesablama qabiliyyəti

🇲🇽 computabilidad

Etymology

The concept of computability has deep roots in mathematical logic and computer science. It emerged in the early 20th century with the work of logicians such as Alan Turing and Alonzo Church. Their groundbreaking contributions laid the foundation for understanding what can and cannot be computed by machines. The study of computability has since become a fundamental aspect of theoretical computer science, shaping the development of algorithms and programming languages.

See also: computable, computation, computational, compute, computed, computer, computerize, computerizing, computing, miscompute.