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Complexity class

As explained in How Large Language Models Work

A complexity class is a category containing problems characterized by the computational resources or algorithmic complexity needed to solve them.

A complexity class groups problems by the kinds of algorithms and computational resources needed to solve them. P and NP are broad examples. section 7.4

The distinction matters because a system cannot compute a harder problem faster than its complexity allows. LLM responses fall into TC⁰; longer intermediate reasoning can reach P, but not NP or harder problems. section 7.4

How How Large Language Models Work covers it

How deep it goes
Explains class membership, representative complexities, and LLM limits without developing formal complexity theory.
Examples
Uses package delivery, flight rescheduling, routing, resource allocation, linear programming, integer programming, and prime factorization.
What you can do after
Evaluate/understand why fluent LLM output does not remove underlying computational complexity limits.
How it connects
Connects complexity classes with algorithms, computational complexity, LLMs, token generation, P, NP, and TC⁰.
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Related concepts

This explainer was generated by Manning's knowledge graph from the text of How Large Language Models Work. The section links point to the parts of the book it draws on.