Halting set
= Halting set
{title2=$\Omega(T)$}
The halting set of a <Turing machine> $T$ is the set of inputs on which it eventually halts. For a deterministic machine with a designated terminal state, eventual halting is invariant along every transition edge, even when that edge is traversed backwards. This observation justifies passing from forward computations to symmetric equality derivations in a <semigroup presentation>.