Krivine machines and higher-order schemes

Sylvain Salvati (1, 2) , Igor Walukiewicz (2)

1 SIGNES - Linguistic signs, grammar and meaning: computational logic for natural language
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

We propose a new approach to analysing higher-order recursive schemes. Many results in the literature use automata models generalising pushdown automata, most notably higher-order pushdown automata with collapse (CPDA). Instead, we propose to use the Krivine machine model. Compared to CPDA, this model is closer to lambda-calculus, and incorporates nicely many invariants of computations, as for example the typing information. The usefulness of the proposed approach is demonstrated with new proofs of two central results in the field: the decidability of the local and global model checking problems for higher-order schemes with respect to the mu-calculus.

Domaines: Logique en informatique [cs.LO]

Sylvain Salvati, Igor Walukiewicz. Krivine machines and higher-order schemes. ICALP, 2011, Switzerland. pp.162-173. ⟨hal-00570017v2⟩