CS theorist explains the two meanings of 'exponential time' behind new 3-SAT result
aran_nayebi · x · 2026-10-31
Responding to new results on solving 3-SAT in subexponential time, theorist TCzajka explains why 'exponential time' is ambiguous in complexity theory.
- Two distinct notions: class E (2^O(n), i.e. O(c^n)) vs. the much broader EXPTIME (O(2^(n^k))) — the latter is 'a misnomer' (exponential of a polynomial) but standard because it's closed under polynomial-time reductions; every NP problem sits in EXPTIME.
- Subexponential time likewise has competing definitions (e.g. 2^o(n), meaning faster than any O(c^n)), and conclusions differ sharply depending on which one a result uses.
- The thread aims to clear up confusion in how the new 3-SAT result gets reported.
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