computational complexity

USAGE SUMMARY

"computational complexity" is correct and usable in written English.
You can use it any time you want to refer to the difficulty of a task or problem that must be solved using a computer. For example: "The computational complexity of simulating quantum systems requires some of the most powerful computers available today."

✓ Grammatically correct

Academia

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

Fall 2011 : Computational Complexity.

University of California, Berkeley

Computational Complexity and Knowledge Complexity.

University of California, Berkeley

Juris Hartmanis: Computational complexity theory.

Cornell University

implying severe computational complexity.

IFAC Proceedings Volumes

Lower Bounds in Computational Complexity, Fall 2018.

University of California, Berkeley

An introduction to computational complexity theory.

Stanford University

) Introduction to research in computational complexity theory.

Princeton University

He works in computational complexity theory.

University of California, Berkeley

Fall 2004: COS522: Computational Complexity Theory.

Princeton University

1980 Steven Fortune, "Topics in Computational Complexity".

Cornell University

Computational Complexity of Sparse Rational Interpolation.

University of California, Berkeley

Expert writing Tips

Best practice

When discussing the "computational complexity" of an algorithm, clearly specify whether you are referring to time complexity, space complexity, or another relevant measure. This adds precision and avoids ambiguity.

Common error

Avoid using "computational complexity" loosely to mean general difficulty. This term has a specific technical meaning related to algorithms and resource usage; use more general terms like 'difficulty' or 'intricacy' for non-computational contexts.

Linguistic Context

The phrase "computational complexity" functions primarily as a noun phrase. It identifies a field of study or a characteristic of algorithms related to the resources they consume. As Ludwig AI explains, it accurately describes the difficulty of tasks solved by computers.

Expression frequency: Very common

Frequent in

Science

45%

Academia

40%

News & Media

15%

Less common in

Formal & Business

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

The phrase "computational complexity" is a well-established term referring to the difficulty of computational problems, as Ludwig AI confirms. Predominantly used in scientific and academic contexts, it describes the resources (time, space) required to solve a problem or execute an algorithm. Understanding the nuances of this concept enables more precise communication in technical discussions. Related phrases such as "algorithmic complexity", "time complexity", and "space complexity" offer alternative perspectives depending on the context. Common pitfalls include using it loosely, instead of using it with the right and precise techincal meaning. Ludwig's examples demonstrate the breadth of its application, solidifying its role as a fundamental term in computer science and related fields.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

algorithmic complexity

Focuses specifically on the complexity inherent in an algorithm.

time complexity

Specifically refers to the amount of time required by an algorithm to complete.

space complexity

Refers to the amount of memory space required by an algorithm.

algorithmic efficiency

Highlights the efficiency (or lack thereof) of an algorithm, relating to complexity.

resource requirements

Emphasizes the resources needed for a computation, a component of complexity.

processing overhead

Refers to the additional processing time or resources needed, akin to complexity.

computational cost

Highlights the cost associated with a computation, related to its complexity.

problem difficulty

Broader term referring to how hard a computational problem is to solve.

task complexity

General term that refers to how intricate or complicated a task is.

computational burden

Refers to the load or strain imposed by a computation, tied to its complexity.

FAQs

How is "computational complexity" measured?

Computational complexity is typically measured using Big O notation, which describes how the resources required (time or space) grow as the input size increases. Common examples include O(n), O(n log n), and O(n^2).

What is the difference between "time complexity" and "space complexity"?

"Time complexity" refers to the amount of time an algorithm takes to run as a function of the input size, while "space complexity" refers to the amount of memory it requires.

What does it mean for a problem to have high "computational complexity"?

A problem with high "computational complexity" requires significant computational resources (time, memory) to solve, especially as the input size grows. This can make it impractical to solve large instances of the problem.

Are there problems that are impossible to solve due to their "computational complexity"?

Yes, some problems are considered computationally intractable, meaning that no known algorithm can solve them in a reasonable amount of time (e.g., problems in the NP-hard or undecidable classes). Researchers are actively exploring ways to approximate solutions or find efficient algorithms for specific cases.