An optimal construction of Hanf sentences

Benedikt Bollig (1, 2) , Dietrich Kuske (3)

1 LSV - Laboratoire Spécification et Vérification [Cachan]
2 MEXICO - Modeling and Exploitation of Interaction and Concurrency
3 TU - Technische Universität Ilmenau

We give a new construction of formulas in Hanf normal form that are equivalent to first-order formulas over structures of bounded degree. This is the first algorithm whose running time is shown to be elementary. The triply exponential upper bound is complemented by a matching lower bound.

Domaines: Logique [math.LO]

Benedikt Bollig, Dietrich Kuske. An optimal construction of Hanf sentences. Journal of Applied Logic, 2012, 10 (2), pp.179-186. ⟨10.1016/j.jal.2012.01.002⟩. ⟨hal-00776607⟩