Ackermannian and Primitive-Recursive Bounds with Dickson's Lemma

Diego Figueira (1) , Santiago Figueira (2) , Sylvain Schmitz (3) , Philippe Schnoebelen (3)

1 LFCS - Laboratory for the Foundations of Computer Science [Edinburgh]
2 Facultad de Informatica
3 LSV - Laboratoire Spécification et Vérification [Cachan]

Dickson's Lemma is a simple yet powerful tool widely used in termination proofs, especially when dealing with counters or related data structures. However, most computer scientists do not know how to derive complexity upper bounds from such termination proofs, and the existing literature is not very helpful in these matters. We propose a new analysis of the length of bad sequences over (N^k,\leq) and explain how one may derive complexity upper bounds from termination proofs. Our upper bounds improve earlier results and are essentially tight.

Domaines: Logique en informatique [cs.LO]; Complexité [cs.CC]

Diego Figueira, Santiago Figueira, Sylvain Schmitz, Philippe Schnoebelen. Ackermannian and Primitive-Recursive Bounds with Dickson's Lemma. 26th Annual IEEE Symposium on Logic in Computer Science, Jun 2011, Toronto, Canada. p. 269--278, ⟨10.1109/LICS.2011.39⟩. ⟨hal-00609871⟩