First-order reduction
In computer science, a first-order reduction is a very weak type of reduction between two computational problems in computational complexity theory. A first-order reduction is a reduction where each component is restricted to be in the class FO of problems calculable in first-order logic.
Since we have, the first-order reductions are weaker reductions than the logspace reductions.
Many important complexity classes are closed under first-order reductions, and many of the traditional complete problems are first-order complete as well. For example, ST-connectivity is FO-complete for NL, and NL is closed under FO reductions .
