Computability: meaning, definitions and examples

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computability

[ˌkɒmˌpjuː.təˈbɪl.ɪ.ti ]

Definitions

^{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?

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?

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.

Interesting Facts

Historical Origins

In the early 1930s, mathematician Alan Turing introduced the concept of computability through his famous Turing machine model.
The term 'computability' gained significance in the 1950s as computer science began developing as a distinct academic field.
Turing's work laid the foundation for understanding which problems can be solved by computers and which cannot.

Mathematics

The study of computability is closely linked to recursive functions and formal languages, which are essential in understanding programming and algorithms.
Not all mathematical problems are computable; for example, determining if a given program will halt is famously undecidable.
Gödel's incompleteness theorems highlight limits on what can be computed or proven, signaling the boundaries of computability.

Computer Science

Computability theory differentiates between problems that can be solved in a finite amount of steps and those that cannot.
It also influences modern algorithms, particularly in areas like artificial intelligence, where computability determines what machines can learn.
As technology advances, new theories of computability address complexities in quantum computing and other emerging fields.

Philosophy

The question of what can be computed raises profound questions about the nature of reasoning, intelligence, and consciousness.
Philosophers ponder whether human thought processes can be fully replicated by machine computation, leading to debates on AI capabilities.
The limits of computability also illuminate discussions about human creativity and intuition, areas still not fully understood.

Pop Culture

Computability concepts appear in popular sci-fi literature, often exploring themes of AI and the limits of machine intelligence, as seen in works by Isaac Asimov.
Movies like 'The Imitation Game' showcase Turing’s contributions, highlighting the human element behind computability and its ethical implications.
Video games frequently incorporate puzzles that relate to computability, challenging players to think critically, similar to programming logic.

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