P versus NP problem
unsolved problem in computer science about time complexity
The P versus NP problem is a major unsolved problem in theoretical computer science. Informally, it asks whether every decision problem for which a proposed positive answer can be quickly verified can also be quickly solved.
Here, "quickly" means an algorithm exists that solves the task and runs in polynomial time (as opposed to, say, exponential time), meaning the task completion time is bounded above by a polynomial function on the size of the input to the algorithm. The general class of questions that some algorithm can answer in polynomial time is "P" or "class P". For some questions, there is no known way to find an answer quickly, but if provided with an answer, it can be verified quickly. The class of questions where an answer can be verified in polynomial time is "NP", standing for "nondeterministic polynomial time".
An answer to the P versus NP question would determine whether problems that can be verified in polynomial time can also be solved in polynomial time. If P ≠ NP, which is widely believed, it would mean that there are problems in NP that are harder to compute than to verify: they could not be solved in polynomial time, but the answer could be verified in polynomial time.
The problem has been called the most important open problem in computer science. Aside from being an important problem in computational theory, a proof either way would have profound implications for mathematics, cryptography, algorithm research, artificial intelligence, game theory, multimedia processing, philosophy, economics and many other fields.
“P versus NP problem” enters the record as unsolved problem in computer science about time complexity. Crown Archives preserves that source wording while asking what versus, problem and unsolved can confirm, complicate or overturn.
Why this record matters
“P versus NP problem” is worth following because a concise public description often conceals a longer documentary argument. Here, versus, problem and unsolved provides the most credible route into that argument.
Named sources, stable identifiers and responsible institutions provide the strongest route from overview to verifiable evidence. The source revision retrieved here is dated Sep 23, 2026. The linked authority identifier is Q746242. None of the 0 selected statements returned an explicit reference.
The absence of detail may reflect summary conventions rather than a lack of surviving documentation. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
How to read it
Use the entry as an orientation point, then follow its citations and revision history. Names, dates and institutional relationships should be checked against the original record.
- Subject orientation
- Search vocabulary
- Locating named sources
The closest primary source, responsible institution and strongest cited specialist reference.
Three-step research path
- Establish the record: confirm the title “P versus NP problem”, its source revision and the description used here.
- Expand the search: follow P versus NP problem primary sources, P versus NP problem archive and versus research across catalogues and specialist indexes.
- Test the account: compare the strongest cited source with the responsible institution’s current record and note any disagreement.
Questions for further research
- Which source most directly establishes the central claim about “P versus NP problem”?
- What terminology or title could unlock a more precise catalogue search?
- Which institution is responsible for the underlying evidence?
Search terms from this dossier
This entry incorporates text from “P versus NP problem” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.