Standard Lemma guide

NP-hard

adj · 2 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

adj

Meaning 1

A problem H is NP-hard if and only if there is an NP-complete problem L that is polynomial time Turing-reducible to H.

Definition source: English Wiktionary via Wiktextract

Usage: not-comparable

Topics: computing, computing-theory, engineering, mathematics, natural-sciences, physical-sciences, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

adj

Meaning 2

An alternative definition restricts NP-hard to decision problems and then uses polynomial-time many-one reduction instead of Turing reduction.

Definition source: English Wiktionary via Wiktextract

Usage: not-comparable

Topics: computing, computing-theory, engineering, mathematics, natural-sciences, physical-sciences, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.

Across languages

Translations

4 source translations are retained for this English entry.

  • Finnish: NP-kova — hard
  • Finnish: NP-vaikea — hard
  • French: NP-dur — hard
  • Hebrew: NP־קשה — hard