Classical realizability as a classifier for nondeterminism

Guillaume Geoffroy (1, 2)

1 AMU - Aix Marseille Université
2 I2M - Institut de Mathématiques de Marseille

We show how the language of Krivine's classical realizability may be used to specify various forms of nondeterminism and relate them with properties of realizability models. More specifically, we introduce an abstract notion of multi-evaluation relation which allows us to finely describe various nondeterministic behaviours. This defines a hierarchy of computational models, ordered by their degree of nondeterminism, similar to Sazonov's degrees of parallelism. What we show is a duality between the structure of the characteristic Boolean algebra of a realizability model and the degree of nondeterminism in its underlying computational model.

Domaines: Logique en informatique [cs.LO]; Logique [math.LO]

Guillaume Geoffroy. Classical realizability as a classifier for nondeterminism. ACM/IEEE Symposium on Logic in Computer Science, Jul 2018, Oxford, United Kingdom. ⟨10.1145/3209108.3209140⟩. ⟨hal-01802215⟩