For a fixed width $k$ and real exponent $a$, $Solvable mode k a$ means that one finite multitape machine decides $k$-CNF satisfiability in time $C(L+1)^d 2^{an}$, where $L$ is the encoded formula length, $n$ is the number of variables, and $C>0$ and $d$ are fixed constants. This is the meaning of $O^*(2^{an})$ used here. The same machine and constants serve every formula of width at most $k$.

The mode distinguishes exact deterministic decision from randomized decision with two-sided error at most $1/3$. In either mode the step bound holds on every input and, in randomized mode, every random tape. Constants and the machine may depend on $k$ and $a$.