The Exponential Time Hypothesis asserts that there exists a constant $a>0$ such that 3-CNF satisfiability has no deterministic $O^*(2^{an})$ algorithm, where $n$ counts variables. This is the positive-exponent formulation of ETH. In its negation, for each positive exponent there may be a different algorithm.

$Randomized$ is the stronger version excluding bounded-error randomized algorithms. Both are defined as propositions; neither is asserted as an axiom or claimed as a proved theorem.