co-NL ($\mathbf{co}\text{-}\mathbf{NL}$)

$\mathbf{co}\text{-}\mathbf{NL}$ consists of complements of languages in NL.

The Immerman–Szelepcsényi theorem states that $\mathbf{NL}=\mathbf{co}\text{-}\mathbf{NL}$. Its proof uses inductive counting of reachable configurations.

Inductive counting certifies the number of vertices reachable within successively larger path-length bounds. Knowing the exact earlier count lets a logarithmic-space nondeterministic machine certify that no reachable predecessor has been omitted.